A Bibliography of Harmonious Colourings and Achromatic Number
  1. B. D. Acharya, Stable set covers, chromaticity and kernels of a hypergraph, Bulletin of the Allahabad Mathematical Society, 17 (2002), pp. 1-15. MR1981658 (2004h:05086)
  2. A. Aflaki, S. Akbari, K. J. Edwards, D. S. Eskandani, M. Jamaali & M. Ravanbod, On harmonious colourings of trees, Electronic Journal of Combinatorics, 19(1) (2012), #P3 pp. 1-9. MR2880634 (2012m:05118)
  3. M. M. Akbar Ali & J. Vernold Vivin, Harmonious chromatic number of central graph of complete graph families, Journal of Combinatorics, Information and System Sciences, 32 (2007), pp. 221-231.
  4. S. Akbari, J. Kim & A. Kostochka, Harmonious coloring of trees with large maximum degree, Discrete Mathematics, 312 (2012), pp. 1633-1637. MR2901157
  5. J. Akiyama, F. Harary & P. Ostrand, A graph and its complement with specified properties VI: Chromatic and achromatic numbers, Pacific Journal of Mathematics, 104 (1983), pp. 15-27. MR0683724 (84h:05101a)
  6. K. Al-Wahabi, R. Bari, F. Harary & D. Ullman, The edge-distinguishing chromatic number of paths and cycles, in Proceedings of Graph Theory in memory of G. A. Dirac (Sandbjerg, 1985) (eds. L. D. Andersen et al.), Annals of Discrete Mathematics, 41, (1989), pp. 17-22. MR0975987 (90a:05076)
  7. M. G. Araujo-Pardo, J. J. Montellano-Ballesteros &  R. Strausz, On the pseudoachromatic index of the complete graph, Journal of Graph Theory, 66 (2011), pp. 89-97. MR2778722 (2012b:05110)
  8. K. Asdre, K. Ioannidou & S. D. Nikolopoulos, The harmonious coloring problem is NP-complete for interval and permutation graphs, Discrete Applied Mathematics, 155 (2007), pp. 2377-2382. MR2360668 (2008j:05130)
  9. K. Asdre & S. D. Nikolopoulos, NP-completeness results for some problems on subclasses of bipartite and chordal graphs, Theoretical Computer Science, 381 (2007), pp. 248-259. MR2347408 (2008i:68093)
  10. B. Auerbach & R. Laskar, Some coloring numbers for complete $r$-partite graphs, Journal of Combinatorial Theory, Series B, 21 (1976), pp. 169-170. MR0485491 (58 #5321)
  11. R. Balakrishnan, R. Sampathkumar & V. Yegnanarayanan, Extremal graphs in some coloring problems, Discrete Mathematics, 186 (1998), pp. 15-24. MR1623860 (99a:05067)
  12. R. Balasubramanian, V. Raman & V. Yegnanarayanan, On the pseudoachromatic number of join of graphs, International Journal of Computer Mathematics, 80 (2003), pp. 1131-1137. MR2008428 (2004h:05043)
  13. D. G. Beane, N. L. Biggs & B. J. Wilson, The growth rate of the harmonious chromatic number, Journal of Graph Theory, 13 (1989), pp. 291-299. MR1000078 (90d:05094)
  14. R. Bharati, I. Rajasingh, S. M. Arul & Varalakshmi, An approximation algorithm for the achromatic number of hex derived networks, in Informatics Engineering and Information Science (Proceedings of International Conference, ICIEIS 2011, Kuala Lumpur, Malaysia, November 14-16, 2011, Proceedings, Part III) Communications in Computer and Information Science, 253, (ed. Azizah Abd Manaf et al.), Springer, Berlin, Heidelberg (2011), pp. 253-261.
  15. V. N. Bhat-Nayak & M. Shanthi, Achromatic number of $\bigcup_{i=1}^5 K_{n_i}$, in Combinatorial Mathematics and Applications (Proceedings of the International Conference held in honor of Raj Chandra Bose, Calcutta, 1988) (eds. J. K. Ghosh et al.), Sankhyā, Series A, 54, Special Issue, (1992), pp. 71-75. MR1234681
  16. V. N. Bhat-Nayak & M. Shanti, Achromatic numbers of a graph and its complement, Bulletin of the Bombay Mathematical Colloquium, 6 (1989), pp. 9-14.
  17. V. N. Bhave, On the pseudoachromatic number of a graph, Fundamenta Mathematicae, 102 (1979), pp. 159-164. MR0532949 (81i:05065)
  18. H. L. Bodlaender, Achromatic number is NP-complete for cographs and interval graphs, Information Processing Letters, 31 (1989), pp. 135-138. MR0998462 (91a:68121)
  19. B. Bollobás, B. Reed & A. Thomason, An extremal function for the achromatic number, in Graph structure theory (Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, Seattle, 1991) (eds. N. Robertson & P. Seymour), Contemporary Mathematics, 147, Amer. Math. Soc., Providence, RI (1993), pp. 161-165. MR1224703 (94b:05073)
  20. F. Bories, Étude du nombre achromatique de certains graphes (Study of the achromatic number of certain graphs), in Colloque sur la Théorie des Graphes (Paris, 1974) Cahiers du Centre d'Études de Recherche Opérationelle, 17, (1975), pp. 155-171. MR0404031 (53 #7837)
  21. F. Bories, Sur quelques problèmes de colorations complètes de sommets et d'arêtes de graphes et d'hypergraphes (On some problems of complete colourings of vertices and edges of graphs and hypergraphs), Thèse de 3ème cycle, Paris, 1975.
  22. F. Bories & J.-L. Jolivet, On complete colorings of graphs, in Recent Advances in Graph Theory, (Proceedings of Second Czechoslovak Symposium, Prague,1974) (ed. M. Fiedler), Academia, Prague (1975), pp. 75-87. MR0384589 (52 #5463)
  23. A. Bouchet & R. Lopez-Bracho, Decomposition of a complete graph into trails of given lengths, Discrete Mathematics, 42 (1982), pp. 145-152. MR0677048 (83m:05117)
  24. H. Bräsel & V. Hadwich, On the complexity of line-distinguishing-coloring of simple graphs, Preprint No. 96-05, Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, 1996.
  25. R. Brewster, Heuristics for computing the achromatic number of a graph, Manuscript, Victoria, B.C., 1987.
  26. R. Brewster & G. MacGillivray, Homomorphically full graphs, Discrete Applied Mathematics, 66 (1996), pp. 23-31. MR1387675 (97k:05166)
  27. B. E. Brunton, B. J. Wilson & T. S. Griggs, Graphs which have $n / 2$-minimal line-distinguishing colourings, Discrete Mathematics, 155 (1996), pp. 19-26. MR1401354 (97b:05053)
  28. F. Buckley & L. Superville, The ajointed number and graph homomorphism problems, in The Theory and Applications of Graphs (Proceedings of Fourth International Conference on the Theory and Applications of Graphs, Kalamazoo, Michigan, 1980) (eds. G. Chartrand et al.), Wiley, New York (1981), pp. 149-158. MR0634523 (83e:05065)
  29. N. Cairnie & K. J. Edwards, Some results on the achromatic number, Journal of Graph Theory, 26 (1997), pp. 129-136. MR1475893 (98i:68217)
  30. N. Cairnie & K. J. Edwards, The achromatic number of bounded degree trees, Discrete Mathematics, 188 (1998), pp. 87-97. MR1630442 (99e:05048)
  31. D. Campbell, Harmonious and achromatic numbers and related colouring problems in graph theory, M.Sc. Thesis, University of Dundee, 2004.
  32. D. Campbell & K. J. Edwards, A new lower bound for the harmonious chromatic number, Australasian Journal of Combinatorics, 29 (2004), pp. 99-102. MR2037338 (2004k:05081)
  33. L. R. Casse, C. M. O'Keefe & B. J. Wilson, Minimal harmoniously colorable designs, Journal of Combinatorial Designs, 2 (1994), pp. 61-69. MR1258474 (94m:05022)
  34. G. Chartrand & J. Mitchem, Graphical theorems of the Nordhaus-Gaddum class, in Recent trends in Graph Theory (Proceedings of First New York City Graph Theory Conference, New York, 1970) (eds. M. Capobianco, J. B. Frechen & M. Krolik), Lecture Notes in Mathematics, 186, Springer, Berlin (1971), pp. 55-61. MR0289354 (44 #6545)
  35. G. Chartrand, F. Okamoto, Zs. Tusa & P. Zhang, A note on graphs with prescribed complete coloring numbers, Journal of Combinatorial Mathematics and Combinatorial Computing, 73 (2010), pp. 77-84. MR2657316 (2011d:05124)
  36. G. Chartrand & P. Zhang, Chromatic Graph Theory, CRC Press, Boca Raton, Discrete Mathematics and its Applications, 2009.
  37. A. Chaudhary & S. Vishwanathan, Approximation algorithms for the achromatic number, in Proceedings of Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (New Orleans, 1997), ACM, New York (1997), pp. 558-563. MR1447703
  38. A. Chaudhary & S. Vishwanathan, Approximation algorithms for the achromatic number, Journal of Algorithms, 41 (2001), pp. 404-416. MR1869259 (2002j:05139)
  39. J. Chen, I. Kanj, J. Meng, G. Xia & F. Zhang, On the pseudo-achromatic number problem, in Proc. 34th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2008), Durham, UK, 2008 (eds. H. Broersma et al.), Lecture Notes in Computer Science, 5344, Springer, Berlin (2008), pp. 78-89.
  40. J. Chen, I. Kanj, J. Meng, G. Xia & F. Zhang, On the pseudo-achromatic number problem, Theoretical Computer Science, 410 (2009), pp. 818-829. MR2492020 (2010b:68061)
  41. N.-P. Chiang & H.-L. Fu, On the achromatic number of the cartesian product $G_1 \times G_2$, Australasian Journal of Combinatorics, 6 (1992), pp. 111-117. MR1196112 (93h:05073)
  42. C. A. Christen & S. M. Selkow, Some perfect coloring properties of graphs, Journal of Combinatorial Theory, Series B, 27 (1979), pp. 49-59. MR0539075 (80k:05055)
  43. C. R. Cook & A. B. Evans, Graph folding, in Proceedings of 10th Southeastern Conference on Combinatorics, Graph Theory and Computing, Vol. I (Boca Raton, 1979) (eds. F. Hoffman et al.), Congressus Numerantium, 23-24, (1979), pp. 305-314. MR0561057 (81f:05079)
  44. E. Drgas-Burchardt & K. Gibek, Harmonious colourings of graphs, Discrete Applied Mathematics, 217 (2017), pp. 175-184.
  45. K. J. Edwards, The harmonious chromatic number of almost all trees, Combinatorics, Probability and Computing, 4 (1995), pp. 31-46. MR1336654 (96j:05040)
  46. K. J. Edwards, The harmonious chromatic number of bounded degree trees, Combinatorics, Probability and Computing, 5 (1996), pp. 15-28. MR1395690 (97j:05065)
  47. K. J. Edwards, The harmonious chromatic number of bounded degree graphs, Journal of the London Mathematical Society (Series 2), 55 (1997), pp. 435-447. MR1452257 (98h:05074)
  48. K. J. Edwards, The harmonious chromatic number and the achromatic number, in Surveys in Combinatorics, 1997 (Invited papers for 16th British Combinatorial Conference) (ed. R. A. Bailey), LMS Lecture Notes, 241, Cambridge University Press, Cambridge (1997), pp. 13-47. MR1477743 (98k:05065)
  49. K. J. Edwards, A new upper bound for the harmonious chromatic number, Journal of Graph Theory, 29 (1998), pp. 257-261. MR1653825 (2000g:05063)
  50. K. J. Edwards, The harmonious chromatic number of complete $r$-ary trees, Discrete Mathematics, 203 (1999), pp. 83-99. MR1696236 (2000e:05060)
  51. K. J. Edwards, Achromatic number versus pseudoachromatic number: a counterexample to a conjecture of Hedetniemi, Discrete Mathematics, 219 (2000), pp. 271-274. MR1761729 (2001f:05064)
  52. K. J. Edwards, Detachments of complete graphs, Combinatorics, Probability and Computing, 14 (2005), pp. 275-310. MR2138114 (2005m:05195)
  53. K. J. Edwards, Achromatic number of fragmentable graphs, Journal of Graph Theory, 65 (2010), pp. 94-114. MR2724490 (2011i:05072)
  54. K. J. Edwards, Harmonious chromatic number of directed graphs, Discrete Applied Mathematics, 161 (2013), pp. 369-376. MR2998438
  55. K. J. Edwards, Achromatic number of collections of paths and cycles, Discrete Mathematics, 313 (2013), pp. 1856-1860. MR3073112
  56. K. J. Edwards & C. J. H. McDiarmid, New upper bounds on harmonious colorings, Journal of Graph Theory, 18 (1994), pp. 257-267. MR1268774 (95g:05045)
  57. K. J. Edwards & C. J. H. McDiarmid, The complexity of harmonious colouring for trees, Discrete Applied Mathematics, 57 (1995), pp. 133-144. MR1327772 (96b:05161)
  58. R. Edwards, Triangle distinguishing vertex colorings, Undergraduate project, Youngstown State University, Ohio, 1997.
  59. M. Farber, G. Hahn, P. Hell & D. J. Miller, Concerning the achromatic number of graphs, Journal of Combinatorial Theory, Series B, 40 (1986), pp. 21-39. MR0830591 (87f:05070)
  60. B. Fawcett, On infinite full colourings of graphs, Canadian Journal of Mathematics, 30 (1978), pp. 455-457. MR0498206 (58 #16361)
  61. O. Frank, F. Harary & M. J. Plantholt, The line-distinguishing chromatic number of a graph, Ars Combinatoria, 14 (1982), pp. 241-252. MR0683991 (84c:05039)
  62. D. P. Geller & S. T. Hedetniemi, A proof technique in graph theory, in Proof Techniques in Graph Theory (Proceedings of Second Ann Arbor Conference on Graph Theory, Ann Arbor, 1968) (ed. F. Harary), Academic Press, New York (1969), pp. 49-59. MR0253929 (40 #7142)
  63. D. P. Geller & H. V. Kronk, Further results on the achromatic number, Fundamenta Mathematicae, 85 (1974), pp. 285-290. MR0357198 (50 #9666)
  64. D. P. Geller & S. Stahl, The chromatic number and other functions of the lexicographic product, Journal of Combinatorial Theory, Series B, 19 (1975), pp. 87-95. MR0392645 (52 #13462)
  65. J. P. Georges, On the harmonious coloring of collections of graphs, Journal of Graph Theory, 20 (1995), pp. 241-254. MR1348566 (96h:05167)
  66. M. Gionfriddo, Problemi aperti in teoria dei grafi. II. Sul numero acromatico di un grafo (Open problems in graph theory. II. On the achromatic number of a graph), in Proceedings of 5th Workshop on Combinatorics (Messina, Italy, 1999) Rendiconti del Seminario Matematico di Messina. Serie II , 5(21), supplement, Università degli Studi di Messina, Messina (2000), pp. 45-52. MR1762098 (2001c:05055)
  67. N. I. Glebov & A. V. Kostochka, Complexity of computation of some functions of graphs (Russian), Metody Diskretnogo Analiza, 51 (1991), pp. 7-16,112. MR1177378 (94a:05189)
  68. N. I. Glebov & A. V. Kostochka, Complexity of computing some functions on graphs, in Siberian Advances in Mathematics. Selected translations. Siberian Advances in Mathematics, 3, Allerton Press, New York (1993), pp. 87-93. MR1236753
  69. B. Godlin, T. Kotek & J. A. Makowsky, Evaluations of graph polynomials, in Graph-Theoretic Concepts in Computer Science, Proceedings of 34th International Workshop, WG 2008 (Durham, UK) (eds. H. Broersma et al.), Lecture Notes in Computer Science, 5344, Springer, Berlin (2008), pp. 183-194.
  70. N. Goyal & S. Vishwanathan, NP-completeness of undirected Grundy numbering and related problems, Manuscript, Bombay, 1997.
  71. T. S. Griggs & B. J. Wilson, Distance-regular graphs, MH-colourings and MLD-colourings, Discrete Mathematics, 174 (1997), pp. 131-135. MR1477231 (98f:05151)
  72. R. P. Gupta, Bounds on the chromatic and achromatic numbers of complementary graphs, in Recent Progress in Combinatorics (Proceedings of Third Waterloo Conference on Combinatorics, Waterloo, 1968) (ed. W. T. Tutte), Academic Press, New York (1969), pp. 229-235. MR0256930 (41 #1585)
  73. G. Hahn & C. Tardif, Graph homomorphisms: structure and symmetry, in Graph symmetry (Montreal, PQ, 1996) (eds. G. Hahn & G. Sabidussi), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 497, Kluwer, Dordrecht (1997), pp. 107-166. MR1468789 (99c:05091)
  74. M. M. Halldórsson, G. Kortsarz, J. Radhakrishnan &  S. Sivasubramanian, Complete partitions of graphs, manuscript, University of Iceland, 2004.
  75. Shousaku Hara, Complete coloring and the achromatic number of graphs, Thesis, Yokohama National University, Japan, 1999.
  76. Shosaku Hara, Triangurations of closed surfaces with achromatic number 3, in Proceedings of 10th Workshop on Topological Graph Theory (Yokohama National University, 1998) Yokohama Mathematical Journal, 47, Special Issue, (1999), pp. 225-229. MR1732779 (2000j:05032)
  77. Shousaku Hara & Atsuhiro Nakamoto, Achromatic numbers of maximal outerplanar graphs, Manuscript, Yokohama National University/Osaka Kyoiku University, Japan, 1999.
  78. Shosaku Hara & Atsuhiro Nakamoto, Achromatic numbers of maximal outerplanar graphs, Yokohama Mathematical Journal, 49 (2002), pp. 181-186. MR1918024 (2003e:05051)
  79. F. Harary & S. T. Hedetniemi, The achromatic number of a graph, Journal of Combinatorial Theory, 8 (1970), pp. 154-161. MR0253930 (40 #7143)
  80. F. Harary, S. T. Hedetniemi & G. Prins, An interpolation theorem for graphical homomorphisms, Portugaliae Mathematica, 26 (1967), pp. 453-462. MR0272662 (42 #7543)
  81. F. Harary & M. J. Plantholt, Graphs with the line-distinguishing chromatic number equal to the usual one, Utilitas Mathematica, 23 (1983), pp. 201-207. MR0703139 (84h:05045)
  82. W. R. Hare, S. T. Hedetniemi, R. Laskar & J. Pfaff, Complete coloring parameters of graphs, in Proceedings of 16th Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, 1985) (eds. F. Hoffman et al.), Congressus Numerantium, 48, (1985), pp. 171-178. MR0830709 (87h:05088)
  83. I. Havel & J.-M. Laborde, On the harmonious chromatic number of quasistars, Manuscript, Prague and Grenoble, 1996.
  84. S. T. Hedetniemi, Homomorphisms of graphs, Technical Report 03105-42-T, University of Michigan, 1965.
  85. S. T. Hedetniemi, Homomorphisms of graphs and automata, Doctoral Dissertation, University of Michigan, 1966.
  86. S. M. Hedetniemi, S. T. Hedetniemi & T. Beyer, A linear algorithm for the Grundy (coloring) number of a tree, in Proceedings of 13th Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, 1982) (eds. F. Hoffman et al.), Congressus Numerantium, 36, (1982), pp. 351-363. MR0726079 (85b:68041)
  87. S. M. Hegde & L. Priya Castelino, Further results on harmonious colorings of digraphs, AKCE International Journal of Graphs and Combinatorics, 8 (2011), pp. 151-159. MR2895432 (2012k:05135)
  88. S. M. Hegde & L. Priya Castelino, On harmonious colorings of regular digraphs, Journal of Graph Labeling, 1 (2015), pp. 55-63.
  89. P. Hell & D. J. Miller, On forbidden quotients and the achromatic number, in Proceedings of Fifth British Combinatorial Conference (Aberdeen, 1975) (eds. C. St. J. A. Nash-Williams & J. Sheehan), Congressus Numerantium, 15, (1976), pp. 283-292. MR0398901 (53 #2752)
  90. P. Hell & D. J. Miller, Graph with given achromatic number, Discrete Mathematics, 16 (1976), pp. 195-207. MR0441778 (56 #173)
  91. P. Hell & D. J. Miller, Achromatic numbers and graph operations, Discrete Mathematics, 108 (1992), pp. 297-305. MR1189852 (93k:05062)
  92. J. E. Hopcroft & M. S. Krishnamoorthy, On the harmonious coloring of graphs, SIAM Journal on Algebraic and Discrete Methods, 4 (1983), pp. 306-311. MR0711339 (85f:05054)
  93. M. Horňák & Š. Pčola, Achromatic number of $K_5 \times K_n$ for large $n$, Discrete Mathematics, 234 (2001), pp. 159-169. MR1826830 (2001m:05107)
  94. M. Horňák & Š. Pčola, Achromatic number of $K_5 \times K_n$ for small $n$, Czechoslovak Mathematical Journal, 53(128) (2003), pp. 963-988. MR2018843
  95. M. Horňák & J. Puntigán, On the achromatic number of $K_m \times K_n$, in Graphs and other Combinatorial Topics (Proceedings of Third Czechoslovak Symposium on Graph Theory, Prague, 1982) (ed. M. Fiedler), Teubner-Texte zur Math., 59, Teubner, Leipzig (1983), pp. 118-123. MR0737024 (85e:05073)
  96. F. Hughes, On the achromatic number of graphs, M.Sc. Thesis, University of Victoria, B.C., 1994.
  97. F. Hughes & G. MacGillivray, The achromatic number of graphs: a survey and some new results, Bulletin of the Institute of Combinatorics and its Applications, 19 (1997), pp. 27-56. MR1427576 (97k:05079)
  98. K. Ioannidou & S. D. Nikolopoulos, Harmonious coloring on subclasses of colinear graphs, in Proc. 4th International Workshop on Algorithms and Computation (WALCOM 2010), Dhaka, Bangladesh, 2010 (eds. M. S. Rahman & S. Fujita), Lecture Notes in Computer Science, 5942, Springer, Berlin (2010), pp. 136-148.
  99. R. W. Irving & D. F. Manlove, The b-chromatic number of a graph, Discrete Applied Mathematics, 91 (1999), pp. 127-141. MR1670155 (2000a:05079)
  100. J.-L. Jolivet, Graphes parfaits pour une propriété P (Graphs perfect for a property P), in Colloque sur la Théorie des Graphes (Paris, 1974) Cahiers du Centre d'Études de Recherche Opérationelle, 17, (1975), pp. 253-256. MR0404035 (53 #7841)
  101. V. Kaladevi, On harmonious colouring of super subdivision of paths and stars, Bulletin of Pure & Applied Sciences - Mathematics and Statistics, 29e (2010), pp. 337-342. MR2828629
  102. J. Kelly, Difference systems, graph designs, and coloring problems, Journal of Combinatorial Theory, Series B, 30 (1981), pp. 144-165. MR0615310 (82k:05033)
  103. S. Kolay, R. Pandurangan1, F. Panolan, V. Raman & P. Tale, Harmonious Coloring: Parameterized Algorithms and Upper bounds, in Graph-Theoretic Concepts in Computer Science: Proceedings of 42nd International Workshop, WG2016 (Istanbul, Turkey, 2016) Lecture Notes in Computer Science, 9941, Springer, Berlin (2016), pp. 245-256.
  104. G. Kortsarz & R. Krauthgamer, On approximating the achromatic number, in Proceedings of 12th Annual ACM-SIAM Symposium on Discrete Algorithms (Washington, D.C., 2001), ACM, New York (2001), pp. 309-318. MR1958423
  105. G. Kortsarz & R. Krauthgamer, On approximating the achromatic number, SIAM Journal on Discrete Mathematics, 14 (2001), pp. 408-422. MR1857593 (2002k:68072)
  106. G. Kortsarz & S. Shende, Approximating the achromatic number problem on bipartite graphs, in Proceedings of 11th European Symposium on Algorithms (Budapest, 2003) Lecture Notes in Computer Science, 2832, Springer, Berlin (2003), pp. 385-396. MR2085469
  107. G. Kortsarz & S. Shende, An improved approximation of the achromatic number on bipartite graphs, SIAM Journal on Discrete Mathematics, 21 (2007), pp. 361-373. MR2318671 (2009c:68102)
  108. G. Kortsarz, J. Radhakrishnan & S. Sivasubramanian, Complete partitions of graphs, in Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (Vancouver) ACM, New York (2005), pp. 860-869. MR2298341
  109. A. V. Kostochka, The minimum Hadwiger number for graphs with a given mean degree of vertices (Russian), Metody Diskretnogo Analiza, 38 (1982), pp. 37-58. MR0713722 (85c:05018)
  110. T. Kotek, J. A. Makowsky & B. Zilber, On counting generalized colorings, in Proceedings of 22nd International Workshop, CSL 2008, 17th Annual Conference of the EACSL (Bertinoro, Italy) (eds. M. Kaminski & S. Martini), Lecture Notes in Computer Science, 5213, Springer, Berlin (2008), pp. 339-353.
  111. I. Krasikov & Y. Roditty, Bounds for the harmonious chromatic number of a graph, Journal of Graph Theory, 18 (1994), pp. 205-209. MR1258253 (94m:05084)
  112. P. Krysta, Approximation Algorithms for Combinatorial Optimization Problems in Graph Coloring and Network Design, Ph.D. Thesis, University of Saarland, Germany, 2001.
  113. P. Krysta & K. Loryś, New approximation algorithms for the achromatic number, Research report No. 98-1-016, Max-Planck-Institut für Informatik, Saarbrücken, Germany, 1998.
  114. P. Krysta & K. Loryś, Efficient approximation algorithms for the achromatic number, in Proceedings of 7th European Symposium on Algorithms (Prague, 1999) (ed. J. Nešetřil), Lecture Notes in Computer Science, 1643, Springer, Berlin (1999), pp. 402-413. MR1729139 (2000j:05119)
  115. P. Krysta & K. Loryś, Efficient approximation algorithms for the achromatic number, Theoretical Computer Science, 361 (2006), pp. 150-171. MR2252575 (2007f:68250)
  116. M. Kubale, Problem of harmonious coloring of graph vertices (Polish), Zeszyty Naukowe Politechniki Ślaskiej, seria Automatyka, 131 (2000), pp. 103-110.
  117. M. Kubale, Harmoniczne kolorowanie grafów, in Optymalizacja dyskretna. Modele i metody kolorowania grafów (ed. M. Kubale), Wydawnictwa Naukowo-Techniczne, Warsaw (2002), pp. 132-146.
  118. M. Kubale, Harmonious coloring of graphs, in Graph colorings (ed. M. Kubale), Contemporary Mathematics, 352, American Mathematical Society, Providence, R.I. (2004), pp. 95-104. MR2076992
  119. A. Kundrík, The harmonious chromatic number of a graph, in Proceedings of Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity (Prachatice, 1990) (eds. J. Nešetřil & M. Fiedler), Annals of Discrete Mathematics, 51, (1992), pp. 167-170. MR1206261 (94c:05034)
  120. Jaeun Lee & Young-hee Shin, The achromatic number of the union of cycles, Discrete Applied Mathematics, 143 (2004), pp. 330-335. MR2087895 (2005c:05084)
  121. S.-M. Lee & J. Mitchem, An upper bound for the harmonious chromatic number of a graph, Journal of Graph Theory, 11 (1987), pp. 565-567. MR0917204 (88k:05081)
  122. M. Liu & B. Liu, On pseudoachromatic number of graphs, Southeast Asian Bulletin of Mathematics, 35 (2011), pp. 431-438. MR2856389 (2012j:05165)
  123. R. Lopez-Bracho, Études du nombre achromatique des étoiles (Studies of the achromatic number of stars), Thesis, Université de Paris-Sud, 1981.
  124. R. Lopez-Bracho, Le nombre achromatique d'une étoile (The achromatic number of a star), Ars Combinatoria, 18 (1984), pp. 187-194. MR0823844 (87i:05097)
  125. Zhikang Lu, On an upper bound for the harmonious chromatic number of a graph, Journal of Graph Theory, 15 (1991), pp. 345-347. MR1118038 (92d:05065)
  126. Zhikang Lu, The harmonious chromatic number of a complete binary and trinary tree, Discrete Mathematics, 118 (1993), pp. 165-172. MR1230060 (94i:05036)
  127. Zhikang Lu, Estimates of the harmonious chromatic numbers of some classes of graphs (Chinese), Journal of Systems Science and Mathematical Sciences, 13 (1993), pp. 218-223. MR1263181 (94m:05086)
  128. Zhikang Lu, The harmonious chromatic number of a complete 4-ary tree, Journal of Mathematical Research and Exposition, 15 (1995), pp. 51-56. MR1334255 (96j:05043)
  129. Zhikang Lu, The exact value of the harmonious chromatic number of a complete binary tree, Discrete Mathematics, 172 (1997), pp. 93-101. MR1467980 (98e:05043)
  130. Zhikang Lu, Exact value of the harmonious chromatic number of a complete trinary tree, Systems Science and Mathematical Sciences, 11 (1998), pp. 26-31. MR1610504 (98m:05070)
  131. G. MacGillivray & A. Rodriguez, The achromatic number of the union of paths, Discrete Mathematics, 231 (2001), pp. 331-335. MR1821972 (2002a:05106)
  132. E. Maistrelli & D. B. Penman, Some colouring problems for Paley graphs, Discrete Mathematics, 306 (2006), pp. 99-106. MR2202078 (2007c:05078)
  133. J. Makowsky, Connection matrices for MSOL-definable structural invariants, in Proceedings of the 3rd Indian Conference on Logic and Its Applications (Chennai, 2009) (eds. R. Ramanujam & S. Sarukkai), Lecture Notes in Artificial Intelligence, 5378, Springer, Berlin (2009), pp. 51-64.
  134. M. F. Mammana, On the achromatic number of $P(\alpha,K_n)$, $P(\alpha,K_{1,n})$ and $P(\alpha,K_{m,n})$, Utilitas Mathematica, 62 (2002), pp. 61-70. MR1941374 (2003j:05049)
  135. M. F. Mammana, On the harmonious chromatic number of $P(\alpha,K_n)$, $P(\alpha,K_{1,n})$ and $P(\alpha,K_{m,n})$, Utilitas Mathematica, 64 (2003), pp. 25-32. MR2012533
  136. D. Marcu, A note on graphs colouring, Buletinul Institutului Politehnic Bucureşti. Seria Transporturi-Aeronave, 51 (1989), pp. 9-14. MR1096609 (91m:05086)
  137. D. Marcu, Note on the $n$-cycles and their achromatic numbers, Computer Science Journal of Moldova, 10 (2002), pp. 329-332. MR1961850 (2004b:05082)
  138. J. Marszakowska, Harmonious coloring of graphs (Polish), M.Sc. Thesis, Institute of Mathematics, Gdánsk University, Poland, 1998.
  139. A. Máté, A lower estimate for the achromatic number of irreducible graphs, Discrete Mathematics, 33 (1981), pp. 171-183. MR0599080 (82c:05060)
  140. C. J. H. McDiarmid, Colouring random graphs badly, in Graph Theory and Combinatorics (Proceedings of a Conference, Milton Keynes, 1978) (ed. R. J. Wilson), Pitman Research Notes in Mathematics, 34, Pitman, San Francisco (1979), pp. 76-86. MR0587624 (82m:05045)
  141. C. J. H. McDiarmid, Achromatic numbers of random graphs, Mathematical Proceedings of the Cambridge Philosophical Society, 92 (1982), pp. 21-28. MR0662955 (83h:05038)
  142. C. J. H. McDiarmid & Luo Xinhua, Upper bounds for harmonious colorings, Journal of Graph Theory, 15 (1991), pp. 629-636. MR1133815 (92g:05094)
  143. F. Milazzo & V. Vacirca, On the achromatic number of permutation graphs, in Proceedings of First Catania International Combinatorial Conference on Graphs, Steiner Systems and their Applications, Vol. 2 (Catania, 1986) (ed. M. Gionfriddo), Ars Combinatoria, 24B, (1987), pp. 71-76. MR0941790 (89e:05090)
  144. F. Milazzo & V. Vacirca, On the achromatic number of $G \times K_m$, in Proceedings of First Catania International Combinatorial Conference on Graphs, Steiner Systems and their Applications, Vol. 2 (Catania, 1986) (ed. M. Gionfriddo), Ars Combinatoria, 24B, (1987), pp. 173-177. MR0941798 (89d:05076)
  145. Z. Miller, Extremal regular graphs for the achromatic number, Discrete Mathematics, 40 (1982), pp. 235-253. MR0676729 (84b:05048)
  146. Z. Miller & D. Pritikin, The harmonious coloring number of a graph, in Proceedings of 250th Anniversary Conference on Graph Theory (Fort Wayne, Indiana, 1986) (eds. K. S. Bagga et al.), Congressus Numerantium, 63, (1988), pp. 213-228. MR0988653 (90b:05055)
  147. Z. Miller & D. Pritikin, The harmonious coloring number of a graph, Discrete Mathematics, 93 (1991), pp. 211-228. MR1139582 (93g:05052)
  148. J. Mitchem, On the harmonious chromatic number of a graph, Discrete Mathematics, 74 (1989), pp. 151-157. MR0989131 (90b:05056)
  149. J. Mitchem & E. Schmeichel, The harmonious chromatic number of deep and wide complete $n$-ary trees, in The Ninth Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms and Applications (Kalamazoo, Michigan, 2000) (eds. Y. Alavi, D. Jones, D. R. Lick and Jiuqiang Liu), Electronic Notes in Discrete Mathematics, 11 (2002). pp. 1-12. MR2155786
  150. D. E. Moser, The star chromatic number and the harmonious chromatic numbers of a graph, Ph.D. Thesis, Purdue University, 1993.
  151. D. E. Moser, Mixed Ramsey numbers: harmonious chromatic number versus independence number, Journal of Combinatorial Mathematics and Combinatorial Computing, 25 (1997), pp. 55-63. MR1480790 (98e:05080)
  152. F. A. Muntaner-Batle, J. Vernold Vivin & M. Venkatachalam, Harmonious coloring on corona product of complete graphs, National Academy Science Letters, 37 (2014), pp. 461-465. MR3265992
  153. G. Prins, Complete contractions of graphs, Manuscript, Antwerp, 1963.
  154. L. W. Rabern, On graph associations, SIAM Journal on Discrete Mathematics, 20 (2006), pp. 529-535. MR2257276 (2007f:05066)
  155. I. Rajasingh, R. Bharati & S. M. Arul, An approximation algorithm for the achromatic number of mesh like topologies, in Proceedings of International Conference on Mathematics and Computer Science (Chennai, 2007) (ed. R. Bharati & I. Rajasingh), Scitech, Chennai (2007), pp. 154-157.
  156. I. Rajasingh, R. Bharati, S. M. Arul & A. William, An approximation algorithm for the achromatic number of mesh like topologies, International Journal of Mathematics and Computer Science, (2007), pp. 155-162. MR2345017
  157. F. Regonati & N. Zagaglia Salvi, Some constructions of $\lambda$-minimal graphs, Czechoslovak Mathematical Journal, 44(119) (1994), pp. 315-323. MR1281026 (95e:05048)
  158. F. Regonati & N. Zagaglia Salvi, Minimal semicomplete graphs, in Proceedings of International Conference on Graphs and Hypergraphs (Varenna, 1991) (eds. O. D'Antona, M. Gionfriddo & N. Zagaglia Salvi), Journal of Combinatorics, Information and System Sciences, 19, Forum for Interdisciplinary Mathematics, Delhi (1994), pp. 63-73. MR1358644 (96f:05107)
  159. Y. Roichman, The achromatic number of trees, grids and cubes, M.Sc. Thesis, Hebrew University of Jerusalem, 1991.
  160. Y. Roichman, On the achromatic number of boolean cubes, Manuscript, Bar-Ilan University, Israel, 1998.
  161. Y. Roichman, On the achromatic number of hypercubes, Journal of Combinatorial Theory, Series B, 79 (2000), pp. 177-182. MR1769195 (2001b:05092)
  162. E. Sampathkumar & V. N. Bhave, Partition graphs and coloring numbers of a graph, Discrete Mathematics, 16 (1976), pp. 57-60. MR0505759 (58 #21763)
  163. M. Shanthi, Achromatic numbers, Ph.D. Thesis, University of Bombay, 1990.
  164. M. T. Shoudy & G. E. Stevens, Achromonious graphs, Congressus Numerantium, 208 (2011), pp. 189-197. MR2856332 (2012h:05126)
  165. E. Sopena, Complete oriented colourings and the oriented achromatic number, Discrete Applied Mathematics, 173 (2014), pp. 102-112. MR3202296
  166. K. Thilagavathi, D. Nidha & N. Roopesh, On harmonious colouring of $C(W_n)$ and $C(F_{m,n})$, Electronic Notes in Discrete Mathematics, 33 (2009), pp. 95-99. MR2574618
  167. K. Thilagavathi & N. Roopesh, Achromatic colouring of $C(C_n)$, $C(K_{m,n})$, $C(K_n)$ and split graphs, in Proceedings of International Conference on Mathematics and Computer Science (Chennai, 2007) (ed. R. Bharati & I. Rajasingh), Scitech, Chennai (2007), pp. 158-161.
  168. K. Thilagavathi & N. Roopesh, Achromatic colouring of central graphs and split graphs, Far East Journal of Applied Mathematics, 30 (2008), pp. 359-369. MR2449488 (2009g:05062)
  169. K. Thilagavathi & N. Roopesh, Generalisation of achromatic colouring of central graphs, Electronic Notes in Discrete Mathematics, 33 (2009), pp. 147-152. MR2574625
  170. K. Thilagavathi, K. P. Thilagavathi & N. Roopesh, The achromatic colouring of graphs, Electronic Notes in Discrete Mathematics, 33 (2009), pp. 153-156. MR2574626
  171. K. Thilagavathi & J. Vernold Vivin, Harmonious colouring of graphs, Far East Journal of Mathematical Sciences, 20 (2006), pp. 189-198. MR2218147 (2006m:05221)
  172. K. Thilagavathi & J. Vernold Vivin, Harmonious colouring of cycles, regular graphs, star $n$-leaf, festoon trees and bigraphs, Far East Journal of Mathematical Sciences, 26 (2007), pp. 779-788. MR2359644 (2008g:05080)
  173. K. Thilagavathi, J. Vernold Vivin & B. Anitha, On harmonious colouring of $L[C(K_{1,n})]$ and $L[C(C_n)]$, in Proceedings of International Conference on Mathematics and Computer Science (Chennai, 2007) (ed. R. Bharati & I. Rajasingh), Scitech, Chennai (2007), pp. 189-194.
  174. K. Thilagavathi, J. Vernold Vivin & B. Anitha, Circumdetic graphs, Far East Journal of Applied Mathematics, 26 (2007), pp. 191-201. MR2306077 (2008b:05054)
  175. J. Vernold Vivin, Harmonious colouring of total graphs, $n$-leaf, central graphs and circumdetic graphs, Ph.D. Thesis, Bharathiar University, India, 2007.
  176. J. Vernold Vivin & M. M. Akbar Ali, On harmonious coloring of middle graph of $C(C_n)$, $C(K_{1,n})$ and $C(P_n)$., Note di Matematica, 29 (2009), pp. 201-211. MR2789821 (2011m:05125)
  177. J. Vernold Vivin, M. M. Akbar Ali & K. Kaliraj, On harmonious coloring of total graphs of $C(C_n)$, $C(K_{1,n})$ and $C(P_n)$., Proyecciones, 29 (2010), pp. 57-75. MR2652272 (2011g:05108)
  178. J. Vernold Vivin, M. M. Akbar Ali & K. Thilagavathi, Harmonious colouring on central graphs of odd cycles and complete graphs, in Proceedings of International Conference on Mathematics and Computer Science (Chennai, 2007) (ed. R. Bharati & I. Rajasingh), Scitech, Chennai (2007), pp. 74-78.
  179. J. Vernold Vivin, M. M. Akbar Ali & K. Thilagavathi, On harmonious coloring of central graphs, Advances and Applications in Discrete Mathematics, 2 (2008), pp. 17-33. MR2504028 (2010e:05116)
  180. J. Vernold Vivin & K. Kaliraj, Harmonious coloring on double star graph families, Tamkang Journal of Mathematics, 43 (2012), pp. 153-158. MR2948412
  181. J. Vernold Vivin & K. Thilagavathi, On harmonious colouring of line graph of central graph of paths, Applied Mathematical Sciences, 3 (2009), pp. 205-214. MR2487573
  182. J. Vernold Vivin, K. Thilagavathi & B. Anitha, On harmonious colouring of line graph of central graphs of bipartite graphs, Journal of Combinatorics, Information and System Sciences, 32 (2007), pp. 233-240.
  183. J. Vernold Vivin, K. Thilagavathi & B. Anitha, On harmonious colouring of line graph of central graphs of bipartite graphs, Journal of Combinatorics, Information and System Sciences, 33 (2008), pp. 37-44.
  184. J. Vernold Vivin, M. Venkatachalam & M. M. Akbar Ali, A note on achromatic coloring of star graph families, Filomat, 23 (2009), pp. 251-255.
  185. J. Vernold Vivin, M. Venkatachalam & M. M. Akbar Ali, Achromatic coloring on double star graph families, International Journal of Mathematical Combinatorics, 3 (2009), pp. 71-81. MR2589603
  186. B. J. Wilson, Line-distinguishing and harmonious colourings, in Graph Colourings (Proceedings of a Conference on Graph Colourings, Milton Keynes, 1988) (eds. R. Nelson & R. J. Wilson), Pitman Research Notes in Mathematics, 218, Longman Scientific & Technical, Essex (1990), pp. 115-133. MR1210072
  187. B. J. Wilson, Minimal line distinguishing colourings in graphs, in Proceedings of Combinatorics '90 (Gaeta, 1990) (eds. A. Barlotti et al.), Annals of Discrete Mathematics, 52, (1992), pp. 549-558. MR1195836 (93k:05069)
  188. R. M. Wilson, Decomposition of complete graphs into subgraphs isomorphic to a given graph, in Proceedings of Fifth British Combinatorial Conference (Aberdeen, 1975) (eds. C. St. J. A. Nash-Williams & J. Sheehan), Congressus Numerantium, 15, (1976), pp. 647-659. MR0396347 (53 #214)
  189. Shaoji Xu, Relations between parameters of a graph, Discrete Mathematics, 89 (1991), pp. 65-88. MR0893081 (88i:05118)
  190. M. Yannakakis & F. Gavril, Edge dominating sets in graphs, SIAM Journal on Applied Mathematics, 38 (1980), pp. 364-372. MR0579424 (83c:68086)
  191. V. Yegnanarayanan, Concerning pseudocomplete partitioning of graphs, Pure and Applied Mathematika Sciences, 48 (1998), pp. 23-31. MR2157021
  192. V. Yegnanarayanan, The pseudoachromatic number of a graph, Southeast Asian Bulletin of Mathematics, 24 (2000), pp. 129-136. MR1811221 (2001k:05085)
  193. V. Yegnanarayanan, On pseudocoloring of graphs, Utilitas Mathematica, 62 (2002), pp. 199-216. MR1941387 (2003i:05059)
  194. V. Yegnanarayanan, On some extremal graph coloring problems of Nordhaus Gaddum class, Bulletin of the Allahabad Mathematical Society, 14 (1999), pp. 147-158. MR1780893 (2001e:05051)
  195. V. Yegnanarayanan, R. Balakrishnan & R. Sampathkumar, On the existence of graphs with prescribed coloring parameters, Discrete Mathematics, 216 (2000), pp. 293-297. MR1750871 (2000k:05121)
  196. V. Yegnanarayanan, Graph colourings and partitions, Theoretical Computer Science, 263 (2001), pp. 59-74. MR1846917 (2002j:05069)
  197. N. Zagaglia Salvi, A note on the line-distinguishing chromatic number and the chromatic index of a graph, Journal of Graph Theory, 17 (1993), pp. 589-591. MR1242176 (94i:05040)

Related references
  1. M. Aigner & E. Triesch, Irregular assignments and two problems á la Ringel, in Topics in Combinatorics and Graph Theory. Essays in honour of Gerhard Ringel. Papers from Graph Theory Meeting (Oberwolfach, 1990) (eds. R. Bodendiek & R. Henn), Physica-Verlag, Heidelberg (1990), pp. 29-36. MR1100017 (92f:05084)
  2. M. Aigner, E. Triesch & Z. Tusa, Irregular assignments and vertex-distinguishing edge-colorings of graphs, in Proceedings of Combinatorics '90 (Gaeta, 1990) (eds. A. Barlotti et al.), Annals of Discrete Mathematics, 52, (1992), pp. 1-9. MR1195794 (93h:05066)
  3. P. N. Balister, Packing circuits into $K_N$, Combinatorics, Probability and Computing, 10 (2001), pp. 463-499. MR1869841 (2002h:05132)
  4. P. N. Balister, Packing digraphs with directed closed trails, Combinatorics, Probability and Computing, 12 (2003), pp. 1-15. MR1967482 (2004b:05088)
  5. P. N. Balister, B. Bollobás & R. H. Schelp, Vertex distinguishing colorings of graphs with $\Delta(G)=2$, Discrete Mathematics, 252 (2002), pp. 17-29. MR1907743 (2003d:05065)
  6. C. Bazgan, A. Harkat-Benhamdine, H. Li & M. Woźniak, On the vertex-distinguishing proper edge-colorings of graphs, Research Report No. 1129, Laboratoire de Recherche en Informatique, Université de Paris Sud, 1997.
  7. C. Bazgan, A. Harkat-Benhamdine, H. Li & M. Woźniak, On the vertex-distinguishing proper edge-colorings of graphs, Journal of Combinatorial Theory, Series B, 75 (1999), pp. 288-301. MR1676894 (2000a:05075)
  8. C. Bazgan, A. Harkat-Benhamdine, H. Li & M. Woźniak, A note on the vertex-distinguishing proper coloring of graphs with large minimum degree, Discrete Mathematics, 236 (2001), pp. 37-42. MR1830596 (2002a:05090)
  9. M. Boguszak, S. Poljak & J. Tuma, Note on homomorphism interpolation theorem, Commentationes Mathematicae Universitatis Carolinae, 17 (1976), pp. 105-109. MR0409202 (53 #12964)
  10. B. Bollobás, P. A. Catlin & P. Erdős, Hadwiger's conjecture is true for almost all graphs, European Journal of Combinatorics, 1 (1980), pp. 195-199. MR0593989 (82b:05107)
  11. F. Bories & J.-L. Jolivet, The achromatic number of a hypergraph, in Proceedings of Fifth British Combinatorial Conference (Aberdeen, 1975) (eds. C. St. J. A. Nash-Williams & J. Sheehan), Congressus Numerantium, 15, (1976), pp. 91-100. MR0406845 (53 #10631)
  12. J. Bosák & J. Nešetřil, Complete and pseudocomplete colourings of a graph, Mathematica Slovaca, 26 (1976), pp. 171-184. MR0439672 (55 #12558)
  13. A. Bouchet, Indice achromatique des graphes multiparti complets et reguliers (Achromatic index of complete regular multipartite graphs), Cahiers du Centre d'Études de Recherche Opérationelle, 20, (1978), pp. 331-340. MR0543176 (82e:05066)
  14. F. Buckley & F. Harary, The chromatic and achromatic status of a graph, Graph Theory notes of New York, 38 (2000), pp. 25-28. MR1751022 (2000k:05108)
  15. F. Buckley & A. J. Hoffman, On the mixed achromatic number and other functions of graphs, in Graph theory and related topics (Proceedings of Conference in honour of W. T. Tutte, Waterloo, Ontario, 1977) (eds. J. A. Bondy & U. S. R. Murty), Academic Press, New York (1979), pp. 105-119. MR0538039 (81f:05123)
  16. F. Buckley & L. Superville, Extremal results for the ajointed number, in Proceedings of 12nd Southeastern Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, 1981) Congressus Numerantium, 32, (1981), pp. 163-171. MR0681877 (84i:05063)
  17. A. C. Burris, On graphs with irregular coloring number 2, Congressus Numerantium, 100 (1994), pp. 129-140. MR1382313 (96k:05054)
  18. A. C. Burris, The irregular coloring number of a tree, Discrete Mathematics, 141 (1995), pp. 279-283. MR1336691 (96a:05054)
  19. A. C. Burris & R. H. Schelp, Vertex-distinguishing proper edge-colorings, Journal of Graph Theory, 26 (1997), pp. 73-82. MR1469354 (99g:05073)
  20. J. Černý, M. Horňák & R. Soták, Observability of a graph, Mathematica Slovaca, 46 (1994), pp. 21-31. MR1414406 (97k:05070)
  21. G. Chen, G. S. Domke, J. H. Hattingh & R. C. Laskar, On the upper line-distinguishing and upper harmonious chromatic numbers of a graph, Journal of Combinatorial Mathematics and Combinatorial Computing, 31 (1999), pp. 227-239. MR1726963 (2000g:05062)
  22. N.-P. Chiang, The achromatic numbers of some uniform hypergraphs, in Proceedings of 25nd Southeastern Conference on Combinatorics, Graph Theory and Computing (Boca Raton, 1994) Congressus Numerantium, 100, (1994), pp. 245-250. MR1382323 (96k:05057)
  23. N.-P. Chiang & H.-L. Fu, The achromatic indices of the regular complete multipartite graphs, Discrete Mathematics, 141 (1995), pp. 61-66. MR1336673 (96a:05056)
  24. N.-P. Chiang & H.-L. Fu, On upper bounds for the pseudo-achromatic index, Discrete Mathematics, 175 (1997), pp. 79-86. MR1475840 (98f:05058)
  25. R. J. Cichelli, Minimal perfect hash functions made simple, Communications of the Association for Computing Machinery, 23 (1980), pp. 17-19.
  26. E. H. Cockayne & S. T. Hedetniemi, Interpolation systems, in Proceedings of Third Southeastern Conference on Combinatorics, Graph Theory and Computing (Boca Raton, 1972) (eds. F. Hoffman et al.), Congressus Numerantium, 6, (1972), pp. 117-129. MR0376414 (51 #12590)
  27. E. H. Cockayne, G. G. Miller & G. Prins, An interpolation theorem for partitions which are complete with respect to hereditary properties, Journal of Combinatorial Theory, Series B, 13 (1972), pp. 290-297. MR0309743 (46 #8848)
  28. C. J. Colbourn & M. J. Colbourn, Greedy colourings of Steiner triple systems, in Proceedings of Combinatorics '81 (Rome, 1981) (eds. A. Barlotti, P. Vittorio Ceccherini & G. Tallini), Annals of Discrete Mathematics, 18, (1983), pp. 201-207. MR0695809 (84f:05030)
  29. P. Dukes, G. MacGillivray & K. Parton, Bounds on the achromatic number of partial triple systems, Contributions to Discrete Mathematics, 2 (2007), pp. 1-12. MR2291880 (2008d:05031)
  30. T. Dvořak , I. Havel & P. Liebl, Euler cycles in the complete graph $K_{2 m + 1}$, Discrete Mathematics, 171 (1997), pp. 89-102. MR1454443 (98c:05103)
  31. T. Dvořak , I. Havel & P. Liebl, Euler cycles in $K_{2 m}$ plus perfect matching, European Journal of Combinatorics, 20 (1999), pp. 227-232. MR1687243 (2000a:05139)
  32. P. Erdős, W. R. Hare, S. T. Hedetniemi & R. Laskar, On the equality of the Grundy and ochromatic numbers of a graph, Journal of Graph Theory, 11 (1987), pp. 157-159. MR0889347 (88g:05057)
  33. P. Erdős, S. T. Hedetniemi, R. C. Laskar & G. C. E. Prins, On the equality of the partial Grundy and upper ochromatic numbers of graphs, Discrete Mathematics, 272 (2003), pp. 53-64. MR2019200 (2004i:05048)
  34. A. B. Evans, Absolutely 3-chromatic graphs, Journal of Graph Theory, 10 (1986), pp. 511-521. MR0867214 (88a:05064)
  35. O. Favaron, H. Li & R. H. Schelp, Strong edge colorings of graphs, Discrete Mathematics, 159 (1996), pp. 103-109. MR1415285 (97e:05087)
  36. Guo-Gang Gao & G. Hahn, Minimal graphs that fold onto $K_n$, Discrete Mathematics, 142 (1995), pp. 277-280. MR1341452 (96f:05100)
  37. J. Ghoshal, R. Laskar & D. Pillone, Minimal rankings, Networks, 28 (1996), pp. 45-53. MR1409775 (97e:05110)
  38. J. Ghoshal, R. Laskar & D. Pillone, Further results on minimal rankings, Ars Combinatoria, 52 (1999), pp. 181-198. MR1705647 (2000f:05036)
  39. T. Gustavsson, Finding a triangle decomposition of a large graph with high minimum degree, Report No. 35, Department of Mathematics, Stockholm University, 1987.
  40. T. Gustavsson, Decompositions of large graphs and digraphs with high minimum degree, Doctoral Dissertation, Stockholm University, 1991.
  41. M. M. Halldórsson, Approximating discrete collections via local improvements, in Proceedings of Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, 1995), ACM, New York (1995), pp. 160-169. MR1321847 (95k:90067)
  42. F. Harary, Conditional colorability in graphs, in Graphs and Applications (Proceedings of First Colorado Symposium on Graph Theory, Boulder, Colorado, 1982) (eds. F. Harary & J. S. Maybee), Wiley, New York (1985), pp. 127-136. MR0778402 (86m:05042)
  43. F. Harary, Maximum versus minimum invariants for graphs, Journal of Graph Theory, 7 (1983), pp. 275-284. MR0710904 (85e:05099)
  44. F. Harary & M. J. Plantholt, The point-distinguishing chromatic index, in Graphs and Applications (Proceedings of First Colorado Symposium on Graph Theory, Boulder, Colorado, 1982) (eds. F. Harary & J. S. Maybee), Wiley, New York (1985), pp. 147-162. MR0778404 (86d:05049)
  45. F. Harary & M. J. Plantholt, Extremal values for chromatic invariants, Matematiche (Catania), 38 (1983), pp. 65-72. MR0924094 (89h:05031)
  46. J. H. Hattingh, M. A. Henning & E. Ungerer, Upper line-distinguishing and upper harmonious chromatic numbers of cycles, Journal of Combinatorial Mathematics and Combinatorial Computing, 45 (2003), pp. 137-144. MR1982641 (2004e:05075)
  47. J. H. Hattingh, M. A. Henning & E. Ungerer, Graphs with small upper line-distinguishing and upper harmonious chromatic numbers, Journal of Combinatorial Mathematics and Combinatorial Computing, 47 (2003), pp. 165-181. MR2019422 (2005c:05082)
  48. S. T. Hedetniemi, Some interpolation theorems for partitions of graphs, Technical Report 03105-47-T, University of Michigan, 1967.
  49. Z. Hedrlin, P. Hell & C. S. Ko, Homomorphism interpolation and approximation, in Algebraic and Geometric Combinatorics (North-Holland Math. Stud. 65) (ed. E. Mendelsohn), Annals of Discrete Mathematics, 15, North-Holland, Amsterdam/New York (1982), pp. 213-227. MR0772597 (86a:05048)
  50. M. Horňák, Achromatic index of $K_{12}$, Ars Combinatoria, 45 (1997), pp. 271-275. MR1447777 (97m:05097)
  51. M. Horňák & R. Soták, Observability of complete multipartite graphs with equipotent parts, Ars Combinatoria, 41 (1995), pp. 289-301. MR1365173 (96g:05058)
  52. M. Horňák & R. Soták, The 5th jump of the point-distinguishing chromatic index of $K_{n,n}$, Ars Combinatoria, 42 (1996), pp. 233-242. MR1386944 (96m:05086)
  53. M. Horňák & R. Soták, Localization of jumps of the point-distinguishing chromatic index of $K_{n,n}$, Discussiones Mathematicae. Graph Theory, 17 (1997), pp. 243-251. MR1627943 (99b:05059)
  54. M. Horňák & R. Soták, Asymptotic behaviour of the observability of $Q_n$, Discrete Mathematics, 176 (1997), pp. 139-148. MR1477284 (99b:05058)
  55. M. Horňák, R. Soták & M. Woźniak, On the achromatic index of $K_{q^2+q+2}$ for a prime $q$, Graphs and Combinatorics, 20 (2004), pp. 191-203. MR2080106 (2006d:05070)
  56. S. G. Indžejan, On the achromatic number of hypergraphs (Russian), Akademiya Nauk Armyanskoĭ SSR Doklady, 69 (1979), pp. 82-87. MR0564134 (81d:05060)
  57. J. Ivančo, Characteristic numbers of partitions of independence systems, Discussiones Mathematicae, 12 (1993), pp. 5-19. MR1221866 (94b:05045)
  58. R. E. Jamison, On the edge achromatic numbers of complete graphs, Discrete Mathematics, 74 (1989), pp. 99-115. MR0989126 (90c:05087)
  59. R. E. Jamison, On the achromatic index of $K_{12}$, in Proceedings of 22nd Southeastern Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, 1991) (eds. F. Hoffman et al.), Congressus Numerantium, 81, (1991), pp. 143-148. MR1152043 (93b:05058)
  60. E. Jucovič & F. Olejník, On chromatic and achromatic numbers of uniform hypergraphs, Časopis Pro Pěstování Matematiky, 99 (1974), pp. 123-130. MR0382053 (52 #2941)
  61. A. Karabeg & D. Karabeg, Graph compaction, Graph Theory notes of New York, 21, (eds. J. W. Kennedy & L. V. Quintas), New York Acad. Sci., New York (1991), pp. 44-51.
  62. A. V. Kostochka, Lower bound of the Hadwiger number of graphs by their average degree, Combinatorica, 4 (1984), pp. 307-316. MR0779891 (86k:05067)
  63. M. Kouider & M. Maheo, The b-chromatic number of a graph, Research report No. 1234, LRI, Université Paris Sud, 1999.
  64. M. Kundríková, Complete colourings of graphs (Slovak), Diploma Thesis, P. J. Šafárik University, Košice, Slovakia, 1985.
  65. R. Lopez-Bracho, Decompositions en chaines d'un graphe complet d'ordre impair (Path decompositions of a complete graph of odd order), in Combinatorial Mathematics (Proceedings of the International Colloquium on Graph Theory and Combinatorics, Marseille-Luminy, 1981) (eds. C. Berge et al.), North-Holland Mathematical Studies, 75, Annals of Discrete Mathematics, 17, (1983), pp. 427-438. MR0841325 (87h:05129)
  66. G. McNulty & W. Taylor, Combinatory interpolation theorems, Discrete Mathematics, 12 (1975), pp. 193-200. MR0385721 (52 #6580)
  67. A. Moukrim, On the minimum number of processors for scheduling problems with communication delays, Annals of Operations Research, 86 (1999), pp. 455-472. MR1683462 (2000a:90026)
  68. C. St. J. A. Nash-Williams, Detachments of graphs and generalised Euler trails, in Surveys in Combinatorics 1985 (Invited papers for Tenth British Combinatorial Conference) (ed. I. Anderson), LMS Lecture Notes, 103, Cambridge University Press, Cambridge (1985), pp. 137-151. MR0822773 (87f:05147)
  69. J. Nešetřil, K. T. Phelps & V. Rödl, On the achromatic number of simple hypergraphs, Ars Combinatoria, 16 (1983), pp. 95-102. MR0734050 (85e:05133)
  70. J. Ninčák, Colourings and hamiltonian cycles (Russian), Dissertation, Minsk, Belarus, 1973.
  71. F. Olejník, Theorems of the Nordhaus-Gaddum type for $k$-uniform hypergraphs, Mathematica Slovaca, 31 (1981), pp. 311-318. MR0621921 (83d:05075)
  72. Liu Sixiang, Lu Yaqin & Ma Longyou, On the total harmonious chromatic number of a graph (Chinese), Journal of Beijing Institute of Civil Engineering and Architecture, 19 (2003), pp. 85-87.
  73. C. M. Turner, R. Rowley, R. E. Jamison & R. Laskar, The edge achromatic number of small complete graphs, in Proceedings of 17th Manitoba Conference on Numerical Mathematics and Computing (Winnipeg, 1987) (eds. D. S. Meek, R. G. Stanton & G. H. J. Van Rees), Congressus Numerantium, 62, (1988), pp. 21-36. MR0961664 (89i:05122)
  74. P. Wittmann, Vertex-distinguishing edge-colorings of 2-regular graphs, Discrete Applied Mathematics, 79 (1997), pp. 265-277. MR1478257 (99a:05128)
  75. N. Zagaglia Salvi, On the point-distinguishing chromatic index of $K_{n,n}$, Ars Combinatoria, 25B (1988), pp. 93-104. MR0942468 (90e:05030)
  76. N. Zagaglia Salvi, A point-distinguishing edge-coloring problem, Rivista di Matematica della Università di Parma (Series 4), 15 (1989), pp. 143-148. MR1064252 (91g:05054)
  77. N. Zagaglia Salvi, On the value of the point-distinguishing chromatic index of $K_{n,n}$, Ars Combinatoria, 29B (1990), pp. 235-244. MR1412879 (97f:05076)
  78. N. Zagaglia Salvi, A problem about the point-distinguishing chromatic index of a cycle, in Combinatorics '88 Vol. 2 (Proceedings of International Conference on Incidence Geometries and Combinatorial Structures, Ravello, 1988) (eds. A. Barlotti et al.), Research and Lecture Notes in Mathematics, Mediterranean Press, Rende (1991), pp. 497-504. MR1223624 (94a:05078)
  79. N. Zagaglia Salvi, The intersection number and point-distinguishing chromatic index of a graph, Vishwa International Journal of Graph Theory, 1 (1992), pp. 103-109. MR1267546 (95c:05056)
  80. N. Zagaglia Salvi, On graphs for which the point-distinguishing chromatic index equals the intersection number, Rivista di Matematica della Università di Parma (Series 4), 4 (1995), pp. 41-47. MR1395322 (97f:05167)
  81. B. Zelinka, Homomorphisms of finite bipartite graphs onto complete bipartite graphs, Mathematica Slovaca, 32 (1982), pp. 361-366. MR0676572 (84b:05050)
  82. B. Zelinka, Homomorphisms of infinite bipartite graphs onto complete bipartite graphs, Czechoslovak Mathematical Journal, 33(108) (1983), pp. 545-547. MR0721085 (85d:05121)
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