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2-Distance choosability of planar graphs with a restriction for maximum degree

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  • Yu, Jiahao
  • Chen, Min
  • Wang, Weifan

Abstract

A proper k-coloring of a graph G is a 2-distance k-coloring of G if each pair of vertices with distance no more than 2 are colored differently. We call G is 2-distance L-colorable if it has a 2-distance coloring π such that π(v)∈L(v), where L={L(v)∣v∈V} is a list assignment of G. Similarly, G is called to be 2-distance k-choosable if there is a 2-distance L-coloring of G such that any list assignment L satisfies |L(v)|≥k for each v∈V(G). The 2-distance list chromatic number of G, denoted by χ2l(G), is the minimum positive integer k such that G is 2-distance k-choosable. In this paper, we prove that every planar graph G with maximum degree Δ has χ2l(G)≤18 if Δ≤5, and χ2l(G)≤4Δ−3 if Δ≥6.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:448:y:2023:i:c:s0096300323001182
    DOI: 10.1016/j.amc.2023.127949
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    References listed on IDEAS

    as
    1. Junlei Zhu & Yuehua Bu, 2018. "Minimum 2-distance coloring of planar graphs and channel assignment," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 55-64, July.
    2. 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.
    3. 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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