The Grr Otzsch Theorem for the Hypergraph of Maximal Cliques
نویسندگان
چکیده
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.
منابع مشابه
Grr Otzsch Theorem for the Hypergraph of Maximal Cliques
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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