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Klesc The crossing numbers of certain Cartesian products
P Mihok and G Semanisin Reducible properties of graphs
E Lazuka On chromaticity of graphs
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1991 Mathematics Subject additive hereditary properties adjacent algorithm assume belongs bipartite graphs Borowiecki choice number chordal graphs chromatic number chromatic polynomial clique complete graph components conjecture consider contradiction Corollary cycle defined denote digraph Discrete Math Discussiones Mathematicae Graph disjoint paths dominating set edge coloring exists Figure finite G and H G contains G V(G graph coloring graph G graph of order HAMILTONIAN CIRCUIT HAMILTONIAN PATH Hence hereditary properties homomorphism implies independent set induced subgraph intersect isomorphic Keywords least Lemma Let G line graph linear list coloring Mathematicae Graph Theory Mathematics Subject Classification matroid maximal graphs maximum Mihok minimal minimum degree neighbor node NP-complete number of edges obtained pair partition permutation graph planar graphs Poland polynomial precoloring problem Proof properties of graphs proved reducible property respectively result set of G subgraph of G subset Suppose Theorem tree Tuza uniquely vertex set vertices of G