## Combinatorics: being the proceedings of the Conference on Combinatorial Mathematics held at the Mathematical Institute, Oxford, Volume 2 |

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2s+l adjacency matrix automorphism B-matching base bipartite graph C0MP0NENT cardinality characteristic polynomial chromatic polynomial coloop colour combinatorial complete graph component condition conjecture contains Corollary corresponding cospectral cycle defined definition denote digraph disjoint from F distributive lattice eigenvalue of G eigenvalues Erdos example exists family F finite graphs finite set four-colour problem generalised graded poset graph G Hamiltonian circuit Hence hyperplane incident independent sets infinite integer intersection irreducible Lemma Let F Let G line graph loop Math Mathematical matrix matroid of rank maximal modular lattice non-empty number of spanning obtained odd circuits ordering function pair partition permutation picture planar planar graph points poset possible problem Proposition prove QM(X rank function regular matroid result satisfies semimodular lattice spanning trees subgraphs submodular supermatroid Suppose symmetric function theory transversal disjoint triples Tutte polynomial valency vector vertex vertices W.T. Tutte