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A sufficient condition on 3-colorable plane graphs without 5- and 6-circuits

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Abstract

In 2003, Borodin and Raspaud proved that if G is a plane graph without 5-circuits and without triangles of distance less than four, then G is 3-colorable. In this paper, we prove that if G is a plane graph without 5- and 6-circuits and without triangles of distance less than 2, then G is 3-colorable.

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Authors and Affiliations

  1. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, 1 Wenyuan Road, Nanjing, 210023, China

    Bao-gang Xu

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  1. Bao-gang Xu
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Correspondence to Bao-gang Xu.

Additional information

Supported by National Natural Science Foundation of China (No.10931003 and 11171160) and by the Doctoral Fund of Ministry of Education of China.

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Xu, Bg. A sufficient condition on 3-colorable plane graphs without 5- and 6-circuits. Acta Math. Appl. Sin. Engl. Ser. 30, 765–772 (2014). https://doi.org/10.1007/s10255-014-0418-4

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  • DOI: https://doi.org/10.1007/s10255-014-0418-4

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