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F Boesch and R Tindell
G Chartrand and R J Wilson
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adjacent algorithms appear applying assigned assume automorphism bipartite graph block graph bound called characterization chromatic number color column competition graph complete components conjecture connected consider construction contains copy corresponding cover cycle defined denote Department of Mathematics determine diameter digraph distinct dual edges elements embedding empire equal exactly example exists fact factor Figure finite four genus give given graph G Graph Theory hamiltonian handles Harary Hence holds independent induced integer interval joining known least Lemma length Let G lines lower Math matrix maximum minimal blocks natural Note obtained packing pair path Petersen graph planar graph plane points possible present problem proof prove question regions regular respectively result satisfies shown snarks splitting subgraph subset Suppose surface Theorem tree University vertex vertices