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Two smaller upper bounds of list injective chromatic number

Author

Listed:
  • Yuehua Bu

    (Zhejiang Normal University)

  • Kai Lu

    (Zhejiang Normal University)

  • Sheng Yang

    (Zhejiang Normal University)

Abstract

An injective coloring of a graph $$G$$ is an assignment of colors to the vertices of $$G$$ so that any two vertices with a common neighbor receive distinct colors. Let $$\chi _{i}^{l}(G)$$ denote the list injective chromatic number of $$G$$ . We prove that (1) $$\chi _{i}^{l}(G)=\Delta $$ for a graph $$G$$ with the maximum average degree $$Mad(G)\le \frac{18}{7}$$ and maximum degree $$\Delta \ge 9$$ ; (2) $$\chi _{i}^{l}(G)\le \Delta +2$$ if $$G$$ is a plane graph with $$\Delta \ge 21$$ and without 3-, 4-, 8-cycles.

Suggested Citation

  • Yuehua Bu & Kai Lu & Sheng Yang, 2015. "Two smaller upper bounds of list injective chromatic number," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 373-388, February.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:2:d:10.1007_s10878-013-9599-7
    DOI: 10.1007/s10878-013-9599-7
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    References listed on IDEAS

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    1. Min Chen & Geňa Hahn & André Raspaud & Weifan Wang, 2012. "Some results on the injective chromatic number of graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 299-318, October.
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