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2-Distance coloring of a planar graph without 3, 4, 7-cycles

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Abstract

A 2-distance coloring of a graph is a coloring of the vertices such that two vertices at distance at most two receive distinct colors. The 2-distance chromatic number \(\chi _{2}(G)\) is the smallest k such that G is k-2-distance colorable. In this paper, we prove that every planar graph without 3, 4, 7-cycles and \(\Delta (G)\ge 15\) is (\(\Delta (G)+4\))-2-distance colorable.

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Acknowledgments

Research supported partially by NSFC (No. 11271334) and ZJNSF (No. Z6110786).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Yuehua Bu & Xia Lv

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  1. Yuehua Bu
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  2. Xia Lv
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Correspondence to Yuehua Bu.

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Bu, Y., Lv, X. 2-Distance coloring of a planar graph without 3, 4, 7-cycles. J Comb Optim 32, 244–259 (2016). https://doi.org/10.1007/s10878-015-9873-y

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  • DOI: https://doi.org/10.1007/s10878-015-9873-y

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