A Bibliography of Harmonious Colourings and Achromatic
Number
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Stable set covers, chromaticity and kernels of a hypergraph,
Bulletin of the Allahabad Mathematical Society,
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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)
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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.
-
S. Akbari, J. Kim & A. Kostochka,
Harmonious coloring of trees with large maximum degree,
Discrete Mathematics,
312
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pp. 1633-1637.
MR2901157
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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)
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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)
-
M. G. Araujo-Pardo, J. J. Montellano-Ballesteros, M. Olsen
& C. Rubio-Montiel,
The diachromatic number of digraphs,
Electronic Journal of Combinatorics,
25(3)
(2018),
pp. 713-724.
MR4221847
-
M. G. Araujo-Pardo, J. J. Montellano-Ballesteros, M. Olsen
& C. Rubio-Montiel,
Achromatic numbers for circulant graphs and digraphs,
Discussiones Mathematicae Graph Theory,
41
(2021),
#P3.51
pp. 1-17.
MR3875016
-
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)
-
M. G. Araujo-Pardo, J. J. Montellano-Ballesteros, R. Strausz
& C. Rubio-Montiel,
On the pseudoachromatic index of the complete graph II,
Boletín de la Sociedad Matemática Mexicana,
20
(2014),
pp. 17-28.
MR3249588
-
M. G. Araujo-Pardo, J. J. Montellano-Ballesteros,
C. Rubio-Montiel & R. Strausz,
On the pseudoachromatic index of the complete graph III,
Graphs and Combinatorics,
34
(2018),
pp. 277-287.
MR3774452
-
S. M. Arul,
On the achromatic number of silicate networks,
International Journal of Pure and Applied Mathematics,
87
(2013),
pp. 771-780.
-
K. Asdre, K. Ioannidou & S. D. Nikolopoulos,
The harmonious coloring problem is NP-complete for interval and
permutation graphs,
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155
(2007),
pp. 2377-2382.
MR2360668 (2008j:05130)
-
K. Asdre & S. D. Nikolopoulos,
NP-completeness results for some problems on subclasses of
bipartite and chordal graphs,
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381
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pp. 248-259.
MR2347408 (2008i:68093)
-
B. Auerbach & R. Laskar,
Some coloring numbers for complete $r$-partite graphs,
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21
(1976),
pp. 169-170.
MR0485491 (58 #5321)
-
R. Balakrishnan, R. Sampathkumar & V. Yegnanarayanan,
Extremal graphs in some coloring problems,
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186
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pp. 15-24.
MR1623860 (99a:05067)
-
R. Balasubramanian, V. Raman & V. Yegnanarayanan,
On the pseudoachromatic number of join of graphs,
International Journal of Computer Mathematics,
80
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pp. 1131-1137.
MR2008428 (2004h:05043)
-
D. G. Beane, N. L. Biggs & B. J. Wilson,
The growth rate of the harmonious chromatic number,
Journal of Graph Theory,
13
(1989),
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MR1000078 (90d:05094)
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R. Bharati, I. Rajasingh, S. M. Arul & Varalakshmi,
An approximation algorithm for the achromatic number of hex
derived networks,
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253,
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pp. 253-261.
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V. N. Bhat-Nayak & M. Shanthi,
Achromatic number of
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Sankhyā, Series A,
54, Special Issue,
(1992),
pp. 71-75.
MR1234681
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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.
-
V. N. Bhave,
On the pseudoachromatic number of a graph,
Fundamenta Mathematicae,
102
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MR0532949 (81i:05065)
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H. L. Bodlaender,
Achromatic number is NP-complete for cographs and interval graphs,
Information Processing Letters,
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pp. 135-138.
MR0998462 (91a:68121)
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B. Bollobás, B. Reed & A. Thomason,
An extremal function for the achromatic number,
in Graph structure theory (Proceedings of the AMS-IMS-SIAM Joint
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MR1224703 (94b:05073)
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F. Bories,
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MR0404031 (53 #7837)
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F. Bories,
Sur quelques problèmes de colorations complètes de
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Thèse de 3ème cycle, Paris,
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F. Bories & J.-L. Jolivet,
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A. Bouchet & R. Lopez-Bracho,
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MR0677048 (83m:05117)
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H. Bräsel & V. Hadwich,
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1996.
-
R. Brewster,
Heuristics for computing the achromatic number of a graph,
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1987.
-
R. Brewster & G. MacGillivray,
Homomorphically full graphs,
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MR1387675 (97k:05166)
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B. E. Brunton, B. J. Wilson & T. S. Griggs,
Graphs which have $n / 2$-minimal line-distinguishing colourings,
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MR1401354 (97b:05053)
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F. Buckley & L. Superville,
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MR0634523 (83e:05065)
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N. Cairnie & K. J. Edwards,
Some results on the achromatic number,
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26
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pp. 129-136.
MR1475893 (98i:68217)
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N. Cairnie & K. J. Edwards,
The achromatic number of bounded degree trees,
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MR1630442 (99e:05048)
-
D. Campbell,
Harmonious and achromatic numbers and related colouring problems
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2004.
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D. Campbell & K. J. Edwards,
A new lower bound for the harmonious chromatic number,
Australasian Journal of Combinatorics,
29
(2004),
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MR2037338 (2004k:05081)
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L. R. Casse, C. M. O'Keefe & B. J. Wilson,
Minimal harmoniously colorable designs,
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2
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MR1258474 (94m:05022)
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G. Chartrand & J. Mitchem,
Graphical theorems of the Nordhaus-Gaddum class,
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G. Chartrand & P. Zhang,
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A. Chaudhary & S. Vishwanathan,
Approximation algorithms for the achromatic number,
in Proceedings of Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
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A. Chaudhary & S. Vishwanathan,
Approximation algorithms for the achromatic number,
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MR1869259 (2002j:05139)
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J. Chen, I. Kanj, J. Meng, G. Xia & F. Zhang,
On the pseudo-achromatic number problem,
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pp. 78-89.
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J. Chen, I. Kanj, J. Meng, G. Xia & F. Zhang,
On the pseudo-achromatic number problem,
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N.-P. Chiang & H.-L. Fu,
On the achromatic number of the cartesian product
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Australasian Journal of Combinatorics,
6
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MR1196112 (93h:05073)
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C. A. Christen & S. M. Selkow,
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27
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C. R. Cook & A. B. Evans,
Graph folding,
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MR0561057 (81f:05079)
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M. Dębski, Z. Lonc & P. Rzążewski,
Achromatic and harmonious colorings of circulant graphs,
Journal of Graph Theory,
87
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MR3729832
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E. Drgas-Burchardt & K. Gibek,
Harmonious colourings of graphs,
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217
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K. J. Edwards,
The harmonious chromatic number of almost all trees,
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MR1336654 (96j:05040)
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K. J. Edwards,
The harmonious chromatic number of bounded degree trees,
Combinatorics, Probability and Computing,
5
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MR1395690 (97j:05065)
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K. J. Edwards,
The harmonious chromatic number of bounded degree graphs,
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55
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MR1452257 (98h:05074)
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K. J. Edwards,
The harmonious chromatic number and the achromatic number,
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MR1477743 (98k:05065)
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K. J. Edwards,
A new upper bound for the harmonious chromatic number,
Journal of Graph Theory,
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MR1653825 (2000g:05063)
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K. J. Edwards,
The harmonious chromatic number of complete $r$-ary trees,
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MR1696236 (2000e:05060)
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K. J. Edwards,
Achromatic number versus pseudoachromatic number:
a counterexample to a conjecture of Hedetniemi,
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MR1761729 (2001f:05064)
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K. J. Edwards,
Detachments of complete graphs,
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K. J. Edwards,
Achromatic number of fragmentable graphs,
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K. J. Edwards,
Harmonious chromatic number of directed graphs,
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MR2998438
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K. J. Edwards,
Achromatic number of collections of paths and cycles,
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MR1327772 (96b:05161)
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K. J. Edwards & P. Rzążewski,
Complete colourings of hypergraphs,
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Triangle distinguishing vertex colorings,
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