Adjacent vertex distinguishing edge colorings of planar graphs with girth at least five

Chengchao Yan, Danjun Huang, Dong Chen and Weifan Wang ()
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Chengchao Yan: Zhejiang Normal University
Danjun Huang: Zhejiang Normal University
Dong Chen: Zhejiang Normal University
Weifan Wang: Zhejiang Normal University

Journal of Combinatorial Optimization, 2014, vol. 28, issue 4, No 13, 893-909

Abstract: Abstract An adjacent vertex distinguishing edge coloring of a graph $$G$$ is a proper edge coloring of $$G$$ such that any pair of adjacent vertices admit different sets of colors. The minimum number of colors required for such a coloring of $$G$$ is denoted by $$\chi ^{\prime }_{a}(G)$$ . In this paper, we prove that if $$G$$ is a planar graph with girth at least 5 and $$G$$ is not a 5-cycle, then $$\chi ^{\prime }_{a}(G)\le \Delta +2$$ , where $$\Delta $$ is the maximum degree of $$G$$ . This confirms partially a conjecture in Zhang et al. (Appl Math Lett 15:623–626, 2002).

Keywords: Adjacent vertex distinguishing edge coloring; Planar graph; Maximum degree; Girth (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10878-012-9569-5

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