An optimal square coloring of planar graphs

Authors:
Yuehua Bu;Xubo Zhu
Affiliations:
Department of Mathematics, Zhejiang Normal University, Jinhua, China;Department of Mathematics, Zhejiang Normal University, Jinhua, China
Venue:
Journal of Combinatorial Optimization
Year:
2012

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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.