## CombinatoricsThis volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation. |

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### Contents

Papers contributed by the participants | 9 |

Constable Positions in Room squares | 23 |

F Escalante Cutset lattices of graphs | 35 |

Copyright | |

11 other sections not shown

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### Common terms and phrases

1-factors 3-polytopes abelian group adjacency matrix affine plane automorphism B-array bicritical bound C*-graphs chromatic number circuit colour column complete Combinatorial Theory complete bipartite graph complete graph complete latin squares conjecture Consider contains Corollary corresponding D. H. Smith define definition disjoint distance-transitive graph duality theorem eigenvalues elements entries equal equation equidistant example exist finite fixed block following theorem function graph G graph theory Halin graph Hamiltonian Harary Hence HISTree homeomorphic implies integer latin rectangle lattice Lemma Let G London Math loops Lovasz matroid node number of vertices obtained partition paths perfect codes planar graphs points polymatroids polynomial positive arrows problem Proof proved r-topes recursive tree regular graphs result row complete latin satisfies semi-stable sequence subgraph of G subsets subspaces symmetric topological space translation plane transversal unit set V-function valency vertex vertices of degree W. T. Tutte Xp(G