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1-extendable 2-packing 5-cycle adjacent algebraic algorithm aliased Anne Penfold Australian bipartite graphs bounds Canada chromatic number clique codes Combinatorics complete bipartite graph complete graph components Computer Science conference conjecture construct contains Corollary cycle define denote Department of Mathematics designs digraph disjoint E. F. Assmus edge graceful edge joining edge-graceful edge-magic labelings Euler Medal Fano plane Figure finite GDPS(m graph G Graph Theory H. F. Mattson Hence Institute of Combinatorics intersection graph isomorphic Kirkman Medals Lemma Let G linear Math matrix maximum minimum starfree biclique orthogonal arrays pair paper partitions Pasch configurations planar graph polynomial polyominoes positive integers problem Professor Proof regular graphs result score sequence self-avoiding semicomplete digraph sphere-of-influence graph starfree biclique decomposition Steiner triple systems strongly regular graph STS(v subgraph subset Suppose symmetric difference Theorem tolerance tournament tree University vectors vertex set vertices walks winners