### 14th British Combinatorial Conference

University of Keele, 5-9 July 1993

#### Contributed talks:

T. Adelgren,
*Triangle-free Eulerian tours in graphs with maximum degree 4*
F. Aguiló (speaker) and M. A. Fiol,
*An efficient algorithm to find optimal double loop networks*
A. Ainouche (speaker) and I. Schiermeyer,
*Neighbourhood intersections and Hamiltonicity*
L. D. Andersen (speaker), H. Fleischner and S. Regner,
*A-trails in outerplane Eulerian graphs*
I. Anderson,
*Cyclic triplewhist tournaments for 4n+1 players*
M. Anthony (speaker), G. Brightwell and C. Cooper,
*On the Vapnik-Chervonenkis dimension of a graph*
R. A. Bailey,
*A Howell design admitting A*_{5}
C. Balbuena (speaker), A. Carmona and M. A. Fiol,
*On digraphs with given sequences of distance connectivities*
S. Ball,
*Blocking sets in finite planes*
J. Bang-Jensen,
*Linking problems for quasi-transitive graphs*
S. G. Barwick (speaker) and C. M. O'Keefe,
*Unitals and inversive planes*
L. M. Batten,
*Blocking sets in PBDs [2,4,1;v]*
B. Bauslaugh,
*Cores and compactness of infinite graphs*
F. K. Bell (speaker) and P. Rowlinson,
*Certain graphs without zero as an eigenvalue*
J. Bierbrauer,
*Universal hashing, geometric codes, orthogonal arrays*
N. L. Biggs,
*The icosian calculus- then and now*
S. Bitan (speaker) and T. Etzion,
*The last packing number of quadruples and cyclic SQS*
R. Bodendiek,
*On labellings of parachutes*
A. Bonisoli,
*On sharply transitive 1-factorizations of K*_{n}
P. Bonizzoni,
*Minimal indecomposable graphs*
C. P. Bonnington,
*Geodesics in infinite transitive graphs*
A. Bowler,
*The fixed points of an automorphism of a symmetric design*
R. Brewster,
*Homomorphisms of edge-coloured graphs to cycles*
M. R. Brito,
*Census of graphs without perfect matching*
I. Broere (speaker), M. Frick, G. Benadé and B. Jonck,
*Uniquely (m,k)-colourable graphs I*
H. J. Broersma (speaker), A. S. Hasratian, J. van den Heuvel
and H. J. Veldman,
*Graphs satisfying a local Ore-type condition*
A. E. Brouwer,
*Bounding the diameter of homogeneous graphs*
M. Buratti,
*Simple radical difference families in Galois fields*
P. J. Cameron,
*The random graph revisited*
A. Carmona (speaker), M. C. Balbuena and M. A. Fiol,
*Maximally distance connected digraphs and bipartite digraphs*
D. V. Chopra,
*On arrays with some combinatorial structure*
E. J. Cockayne,
*On a Nordhaus-Gaddum type problem for independent domination*
F. P. Comellas (speaker), M. A. Fiol and J. Gómez,
*Large vertex symmetric 2-reachable digraphs*
P. Cowling,
*Strong total colouring numbers of complete hypergraphs*
D. Cvetkovic (speaker) and S. Simic,
*On graphs whose second largest eigenvalue does not exceed (sqrt(5) - 1)/2*
J. A. Davis,
*Nonexistence of partial difference sets in abelian p-groups*
U. Dempwolff,
*Translation planes of order 27*
J. Dunbar,
*Nearly perfect sets in graphs*
S. Easton,
*Some necessary conditions for the degree sequence of a highly irregular graph*
M. Escudero (speaker), J. Fàbrega and J. Gómez,
*Edge-colourings of some graphs on alphabets and compound graphs*
M. Espona-Dones (speaker), J. M. Brunat, M. A. Fiol and O. Serra,
*On Cayley line digraphs*
D. Fon-der-Flaass (speaker), M. Axenovitch and A. Kostochka,
*Set systems without weak 3-\Delta-subsystems*
K. Fraughnaugh,
*Size in maximal triangle-free graphs and minimal graphs of diameter two*
M. Frick, G. Benadé, I. Broere and B. Jonck,
*Uniquely (m,k)-colourable graphs II*
C.-M. Fu,
*Graph transformations which preserve the multiplicity of an eigenvalue*
H.-L. Fu,
*On the upper embeddability of diameter three graphs*
V. Giakoumakis (speaker) and J. L. Fouquet,
*On semi-sparse Graphs I*
S. W. Golomb (speaker) and H. Y. Song,
*Cyclic Hadamard difference sets- a status report*
S. J. Goodall,
*The number of posets of width two*
L. Gordeev,
*Strong well-quasi-ordering tree theorems*
M. J. Grannell (speaker), T. S. Griggs and E. Mendelsohn,
*A small basis for four-line configurations in Steiner triple systems*
T. S. Griggs,
*Continuity of Mendelsohn and Steiner triple systems*
H. Gropp,
*On orbital matrices*
G. Gutin (speaker), J. Bang-Jensen and J. Huang,
*A sufficient condition for a complete multipartite digraph to be Hamiltonian*
W. H. Haemers (speaker) and M. J. Coster,
*Quasi-symmetric designs related to the triangular graph*
R.H. Häggkvist (speaker) and A. Johansson,
*(1,2)-factorizations of general Eulerian nearly regular graphs*
F. Harary,
*Destroying the automorphisms of a graph by orientations*
H. Harborth,
*Cube graph Ramsey numbers*
E. R. Harzheim,
*On weakly arithmetic progressions*
M. A. Henning,
*Majority domination in graphs*
J. van den Heuvel (speaker) and R. J. Faudree,
*Degree sums, factors, and cycles in graphs*
R. Hill (speaker), E. R. Berlekamp and J. P. Karim,
*Searching with lies the Ulam problem*
J. W. P. Hirschfeld,
*The combinatorics of finite planes*
S. A. Hobart,
*Krein conditions for coherent configurations*
C. Hoede,
*Graphs and games*
S. C. Hoggar,
*Faster fractal pictures by finite fields*
Jing Huang (speaker), J. Bang-Jensen and G. Gutin,
*Weakly Hamiltonian-connected ordinary multipartite tournaments*
A. Huck,
*On cycle-double-covers of some graphs*
R. Hughes Jones,
*Enumerating uniform polyhedral surfaces with triangular faces*
D. Jennings,
*On packings of squares and rectangles*
M. Jimbo,
*A Hadamard tournament and three person tournament games*
B. Jones,
*Balanced neighbour designs in circular blocks of equal and unequal designs*
L. K. Jørgensen,
*Cayley digraphs with certain properties*
A. D. Keedwell (speaker) and G. Sittampalam,
*Critical sets and critical partial latin squares*
G. B. Khosrovshahi,
*"Trading Signed Design" algorithm and some new designs*
G. Y. Kiss (speaker) and J. W. P. Hirschfeld,
*On cyclic sets in PG(2,4) without tangents*
S. Klavzar,
*Coloring graph products and graph bundles*
J. Koolen (speaker) and S. V. Shpectorov,
*Distance-regular graphs of negative type*
G. Korchmáros,
*A generalization of a theorem by B. Segre*
E. Kubicka,
*Fast algorithms for all trees with an application to designing and evaluation of hierarchical networks*
G. Kubicki,
*Agreement subtrees, metrics and consensus for labelled binary trees*
J.D. Lamb,
*Cubic digraphs containing coenergy covers - a conjecture*
M. Lewin,
*On the sparsity of imprimitive matrices*
R. P. Lewis,
*A combinatorial proof of a theorem about ranks*
E. K. Lloyd,
*Polygonal systems*
J. R. Lundgren,
*Inverting competition graphs*
G. MacGillivray,
*Hereditarily hard H-colouring problems*
E. S. Mahmoodian (speaker) and M. Mirzakhani,
*Decomposition of complete tripartite graphs into pentagons*
M. Mehbali,
*Algebraic computational complexity*
R. Mesliulam,
*Discrete uncertainty inequalities*
K. Metsch,
*Twisted derivations (covering the same pairs of points with distinct sets of lines)*
J. W. Moon (speaker) and A. Meir,
*On path entropy functions for rooted trees*
H. M. Mulder,
*The median procedure*
X. Muñoz,
*Diameter of the surviving route digraph in l-geodetic digraphs and graphs*
C. Mynhardt (speaker), E. J. Cockayne, G. Fricke and S. T.
Hedetniemi,
*Extremum aggregates of hypergraph functions: existence and interpolation theorems*
C. St. J. A. Nash-Williams,
*Strongly connected mixed graphs and connected detachments of graphs*
M. Noy,
*Counting triangulations of non-convex polygons*
S. Oates-Williams (speaker) and D. Bryant,
*Mendelsohn designs associated with certain idempotent quasigroups*
P. Östergård,
*New constructions for q-ary covering codes*
P. J. Owens,
*Non-Hamiltonicity for regular graphs*
C. Padró (speaker) and P. Morillo,
*Diameter-vulnerability of iterated line digraphs*
K. C. Paterson (speaker) and M. J. B. Robshaw,
*Decoding a class of de Bruijn sequences*
R. Peeters,
*Uniqueness of strongly regular graphs with minimal p-rank*
D. A. Preece,
*Partitioning 7 x 7 latin squares into Youden squares*
K. A. S. Quinn,
*Bounds for key distribution patterns*
R. C. Read (speaker) and R. J. Wilson,
*The making of "An Atlas of Graph Theory"*
F. Rivera-Campo,
*A note on spanning trees with bounded degree*
C. A. Rodger (speaker) and E. B. Wantland,
*Embedding edge-colourings into k-factorisations*
Y. Roditty (speaker), Y. Caro and J. Schönheim,
*On colored designs*
Z. Ryjácek (speaker), H. J. Broersma and I. Schiermeyer,
*Toughness and Hamiltonicity in almost claw-free graphs*
A. Sánchez-Arroyo,
*A new bound for total colouring*
E. R. Scheinerman (speaker) and H. Wilf,
*The rectilinear crossing number of a graph and Sylvester's four point problem*
I. Schiermeyer,
*Insertible vertices, neighborhood intersections and Hamiltonicity*
J. Schönheim,
*On sets of pairwise non-coprime divisors of a number*
K. Seyffarth,
*Domination numbers of planar graphs*
A. Shastri,
*Bandwidth of graphs*
R. Shaw,
*The Klein quadric, Conwells heptads (and more)- all inside the Fano 7-point plane*
E. Simó (speaker) and J. L. A. Yebra,
*Vulnerability of the diameter of odd graphs*
D. Singmaster,
*Sliding block puzzles*
D. H. Smith,
*Cut sets and network reliability*
A. Soleev (speaker) and A. D. Bruno,
*Ordering in complicated problems and Newton polyhedra*
H. C. Swart,
*Relations between distance domination parameters of high integrity*
H. J. Thuillier (speaker), D. Delamare and J. L. Fouquet,
*Linear-k-arboricity of cubic graphs*
E. Triesch,
*On the recognition complexity of some graph properties*
Z. Tuza,
*Covering and independence for complete subgraphs*
J. Ueberberg,
*Interactive theorem proving and symbolic incidence geometry*
K. Ushio,
*S*_{5} factorization of complete bipartite graphs
H. J. Veldman,
*When are Hamiltonian line graphs pancyclic?*
P. D. Vestergaard (speaker) and B. Zelinka,
*Domination in graphs*
B. J. Vowden,
*Graeco-Latin squares with embedded balanced superimpositions of Youden rectangles*
C. D. Wakelin,
*The chromatic polynomial relative to the complete graph basis*
J. J. Watkins,
*A Proof of Petersen's theorem on 1-factors in cubic graphs*
B. Webb,
*Cycle decompositions of automorphisms of finite incidence structures*
D. B. West,
*Two problems on acyclic orientations*
J. West (speaker) and N. Ray,
*On a poset of permutation matrices*
C. Whitehead,
*Techniques for constructing well-covered graphs with no 4-cycles*
E. C. Whitehead,
*Chromaticity of K*_{4} homeomorphs
P. R. Wild,
*Some families of semibiplanes*
R. Wilson,
*Renaissance combinatorics*
N. Wormald,
*Differential equations for random graph processes*
J. L. Yucas,
*Some constructions from PG(3,2)*
P. H. Zieschang,
*Structure theory of association schemes*

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