## Ars Combinatoria, Volumes 72-73Department of Combinatorics and Optimization, University of Waterloo., 2004 - Combinatorial analysis |

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3-colorings a(G x H acyclic adjacent algorithm assume attaching set bipartite graph block Bruijn sequences chromatic number Combinatorial complete bipartite graph complete graph Computer conjecture connected graph construction Corollary cut vertex cycle defined denote digraph Discrete Math disjoint dominating set domination number edge-connectivity eigenvalues embedding ex(n exists face labeling Figure follows G and H G contains geodetic set graph G graph of order Graph Theory Hence hypergraph implies independent set induced subgraph integer isomorphic labeling of type latin square Lemma Let G lower bound maximum degree minimum detour set number of edges obtain outerplanar pairs partial colorings partitioned path permutation Petersen graph polynomial positive integer problem Proof Proposition prove Ramsey Number result sat(n sequence of order series-parallel graph set of G Skolem sequence Steiner triple system strongly regular graph subset support vertex Suppose Theorem total dominating set tree dominating set unique vertex set vertices of degree