The Grötzsch Theorems for the Hypergraph of Maximal Cliques
نویسندگان
چکیده
In this paper, we extend the Grötzsch Theorem by proving that the clique hypergraph H(G) of every planar graph is 3-colorable. We also extend this result to list colorings by proving that H(G) is 4-choosable for every planar or projective planar graph G. Finally, 4-choosability of H(G) is established for the class of locally planar graphs on arbitrary surfaces.
منابع مشابه
Coloring the hypergraph of maximal cliques of a graph with no long path
We consider the problem of coloring the vertices of a graph so that no maximal clique of size at least two is monocolored. We solve the following question: Given a ;xed graph F , does there exist an integer f(F) such that the hypergraph of maximal cliques of any F-free graph can be f(F)-colored? We show that the answer is positive if and only if all components of F are paths. In that case we gi...
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In this paper, we extend the Grr otzsch Theorem by proving that the clique hypergraph H(G) of every planar graph is 3-colorable. We also extend this result to list colorings by proving that H(G) is 4-choosable for every planar or projective planar graph G. Finally, 4-choosability of H(G) is established for the class of locally planar graphs on arbitrary surfaces.
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In this paper, we extend the Grötzsch Theorem by proving that the clique hypergraph H(G) of every planar graph is 3-colorable. We also extend this result to list colorings by proving that H(G) is 4-choosable for every planar or projective planar graph G. Finally, 4-choosability ofH(G) is established for the class of locally planar graphs on arbitrary surfaces.
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