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

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Listed:
  • Chengchao Yan

    (Zhejiang Normal University)

  • Danjun Huang

    (Zhejiang Normal University)

  • Dong Chen

    (Zhejiang Normal University)

  • Weifan Wang

    (Zhejiang Normal University)

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).

Suggested Citation

  • Chengchao Yan & Danjun Huang & Dong Chen & Weifan Wang, 2014. "Adjacent vertex distinguishing edge colorings of planar graphs with girth at least five," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 893-909, November.
  • Handle: RePEc:spr:jcomop:v:28:y:2014:i:4:d:10.1007_s10878-012-9569-5
    DOI: 10.1007/s10878-012-9569-5
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    References listed on IDEAS

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    1. Weifan Wang & Yiqiao Wang, 2010. "Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree," Journal of Combinatorial Optimization, Springer, vol. 19(4), pages 471-485, May.
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    Cited by:

    1. Junlei Zhu & Yuehua Bu & Yun Dai, 2018. "Upper bounds for adjacent vertex-distinguishing edge coloring," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 454-462, February.

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