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An improved bound on 2-distance coloring plane graphs with girth 5

Author

Listed:
  • Wei Dong

    (Southeast University
    Nanjing Xiaozhuang University)

  • Wensong Lin

    (Southeast University)

Abstract

A vertex coloring is called $$2$$ 2 -distance if any two vertices at distance at most $$2$$ 2 from each other get different colors. The minimum number of colors in 2-distance colorings of $$G$$ G is its 2-distance chromatic number, denoted by $$\chi _2(G)$$ χ 2 ( G ) . Let $$G$$ G be a plane graph with girth at least $$5$$ 5 . In this paper, we prove that $$\chi _2(G)\le \Delta +8$$ χ 2 ( G ) ≤ Δ + 8 for arbitrary $$\Delta (G)$$ Δ ( G ) , which partially improves some known results.

Suggested Citation

  • Wei Dong & Wensong Lin, 2016. "An improved bound on 2-distance coloring plane graphs with girth 5," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 645-655, August.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:2:d:10.1007_s10878-015-9888-4
    DOI: 10.1007/s10878-015-9888-4
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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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    Cited by:

    1. Junlei Zhu & Yuehua Bu & Miltiades P. Pardalos & Hongwei Du & Huijuan Wang & Bin Liu, 2018. "Optimal channel assignment and L(p, 1)-labeling," Journal of Global Optimization, Springer, vol. 72(3), pages 539-552, November.
    2. Yu, Jiahao & Chen, Min & Wang, Weifan, 2023. "2-Distance choosability of planar graphs with a restriction for maximum degree," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    3. Qiming Fang & Li Zhang, 2022. "Sharp upper bound of injective coloring of planar graphs with girth at least 5," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1161-1198, September.
    4. Hoang La & Mickael Montassier, 2022. "2-Distance list $$(\Delta +2)$$ ( Δ + 2 ) -coloring of planar graphs with girth at least 10," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1356-1375, September.
    5. Wei Dong & Baogang Xu, 2017. "2-Distance coloring of planar graphs with girth 5," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1302-1322, November.

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