An optimal square coloring of planar graphs

Yuehua Bu () and Xubo Zhu
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Yuehua Bu: Zhejiang Normal University
Xubo Zhu: Zhejiang Normal University

Journal of Combinatorial Optimization, 2012, vol. 24, issue 4, No 12, 580-592

Abstract: 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.

Keywords: Planar graphs; Maximum degree; Girth; Square of a graph (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-011-9409-z

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