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An optimal square coloring of planar graphs

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Abstract

The square coloring of a graph is to color the vertices of a graph at distance at most 2 with different colors. In 1977, Wegner posed a conjecture on square coloring of planar graphs. The conjecture is still open. In this paper, we prove that Wegner’s conjecture is true for planar graphs with girth at least 6.

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Authors and Affiliations

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

    Yuehua Bu & Xubo Zhu

Authors
  1. Yuehua Bu
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  2. Xubo Zhu
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Corresponding author

Correspondence to Yuehua Bu.

Additional information

The project was supported by NSFC (Grant No. 10971198) and Zhejiang Innovation Project (T200905), ZSDZZZZXK08.

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Bu, Y., Zhu, X. An optimal square coloring of planar graphs. J Comb Optim 24, 580–592 (2012). https://doi.org/10.1007/s10878-011-9409-z

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  • DOI: https://doi.org/10.1007/s10878-011-9409-z

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