## Ars Combinatoria, Volumes 50-51Department of Combinatorics and Optimization, University of Waterloo., 1998 - Combinatorial analysis |

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acyclic adjacent algorithm assume balanced ternary BIB design bipartite graph blocks cells chordal chordal graphs classes claw-free graph clique column Combinatorial competition graph competition number complete graph components conjecture connected graph consider construction contradiction Corollary covering critical set cubic graph cycle of length define denote digraph Discrete Math disjoint DYRs edges elements exists exp(G exponent Figure finite follows g-centroid graph G graph of order Graph Theory Hamiltonian cycle Hamiltonian path Hence implies induced subgraph interval colouring isolated vertices isomorphism latin square least Lemma Let G matrix maximal maximum matching minimal minimum multigraph non-isomorphic obtain pair parameters partition path perfect matching permutation graphs Petersen graph points positive integer primitive problem projective plane Proposition prove result SBIBD self-packing snarks Steiner triple systems strongly graceful subgraph of G subset Suppose symmetric ternary tree unique vertex set vertices of G