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List 2-distance coloring of planar graphs

Author

Listed:
  • Yuehua Bu

    (Zhejiang Normal University)

  • Xiaoyan Yan

    (Zhejiang Normal University)

Abstract

The $$2$$ 2 -distance coloring of a graph $$G$$ G is to color the vertices of $$G$$ G so that every two vertices at distance at most $$2$$ 2 from each other get different colors. Let $$\chi _{2}^{l}(G)$$ χ 2 l ( G ) be the list 2-distance chromatic number of $$G$$ G . In this paper, we show that (1) a planar graph $$G$$ G with $$\Delta (G)\ge 12$$ Δ ( G ) ≥ 12 which contains no $$3,5$$ 3 , 5 -cycles and intersecting 4-cycles has $$\chi _{2}^{l}(G)\le \Delta +6$$ χ 2 l ( G ) ≤ Δ + 6 ; (2) a planar graph $$G$$ G with $$\Delta (G)\le 5$$ Δ ( G ) ≤ 5 and $$g(G)\ge 5$$ g ( G ) ≥ 5 has $$\chi _{2}^{l}(G)\le 13$$ χ 2 l ( G ) ≤ 13 .

Suggested Citation

  • Yuehua Bu & Xiaoyan Yan, 2015. "List 2-distance coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 1180-1195, November.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:4:d:10.1007_s10878-013-9700-2
    DOI: 10.1007/s10878-013-9700-2
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    References listed on IDEAS

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    1. Yuehua Bu & Xubo Zhu, 2012. "An optimal square coloring of planar graphs," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 580-592, November.
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