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2-Distance coloring of planar graphs without adjacent 5-cycles

Author

Listed:
  • Yuehua Bu

    (Zhejiang Normal University
    Zhejiang Guangsha Vocational and Technical University of Construction)

  • Zewei Zhang

    (Zhejiang Normal University)

  • Hongguo Zhu

    (Zhejiang Normal University)

Abstract

The k-2-distance coloring of graph G is a mapping $$c:V(G)\rightarrow \{1,2,\ldots ,k\}$$ c : V ( G ) → { 1 , 2 , … , k } such that any two vertices at distance at most two from each other get different colors. The 2-distance chromatic number is the smallest integer k such that G has a k-2-distance coloring, denoted by $$\chi _{2}(G)$$ χ 2 ( G ) . In this paper, we prove that every planar graph G without adjacent 5-cycles and $$g(G)\ge 5$$ g ( G ) ≥ 5 and $$\Delta (G)\ge 17$$ Δ ( G ) ≥ 17 has $$\chi _{2}(G)\le \Delta +3$$ χ 2 ( G ) ≤ Δ + 3 .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:5:d:10.1007_s10878-023-01053-2
    DOI: 10.1007/s10878-023-01053-2
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    References listed on IDEAS

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    1. 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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