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2-Distance coloring of planar graphs with girth 5

Author

Listed:
  • Wei Dong

    (Nanjing XiaoZhuang University)

  • Baogang Xu

    (Nanjing Normal University)

Abstract

A vertex coloring is said to be 2-distance if any two distinct vertices of distance at most 2 receive different colors. Let G be a planar graph with girth at least 5. In this paper, we prove that G admits a 2-distance coloring with at most $$\Delta (G)+3$$ Δ ( G ) + 3 colors if $$\Delta (G)\ge 339$$ Δ ( G ) ≥ 339 .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:4:d:10.1007_s10878-017-0148-7
    DOI: 10.1007/s10878-017-0148-7
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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.
    2. 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.
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    Cited by:

    1. 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).
    2. 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.
    3. 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.
    4. Yuehua Bu & Zewei Zhang & Hongguo Zhu, 2023. "2-Distance coloring of planar graphs without adjacent 5-cycles," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-19, July.

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