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On L(p,q)-labelling of planar graphs without cycles of length four

Author

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  • Hou, Jianfeng
  • Jin, Yindong
  • Li, Heng
  • Miao, Lianying
  • Zhao, Qian

Abstract

Let p,q be integers with p≥q≥0 and let G be a graph. A k−L(p,q)−labeling of G is a function φ:V(G)→{0,1,…,k} such that |φ(x)−φ(y)|≥p if xy∈E(G), and |φ(x)−φ(y)|≥q if x and y have at least one common neighbor in G. Suppose that G is a planar graph with maximum degree Δ, and without cycles of length four. We show that λp,q(G)≤(2q−1)Δ+8p+10q−9, which improves the bound given by Zhu, Hou, Chen and Lv [The L(p,q)-labelling of planar graphs without 4-cycles, Discrete Appl. Math. 162 (2014) 355–363].

Suggested Citation

  • Hou, Jianfeng & Jin, Yindong & Li, Heng & Miao, Lianying & Zhao, Qian, 2023. "On L(p,q)-labelling of planar graphs without cycles of length four," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    • Handle: RePEc:eee:apmaco:v:446:y:2023:i:c:s009630032300053x
    DOI: 10.1016/j.amc.2023.127884
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    References listed on IDEAS

    as
    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. Miao Zhang & Min Chen & Yiqiao Wang, 2017. "A sufficient condition for planar graphs with girth 5 to be (1, 7)-colorable," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 847-865, April.
    3. Hou, Jianfeng & Zhu, Hongguo, 2020. "Choosability with union separation of planar graphs without cycles of length 4," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Clément Charpentier & Mickaël Montassier & André Raspaud, 2013. "L(p,q)-labeling of sparse graphs," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 646-660, May.
    5. Min Chen & Yingying Fan & Yiqiao Wang & Weifan Wang, 2017. "A sufficient condition for planar graphs to be (3, 1)-choosable," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 987-1011, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    L(p; q)-coloring; Planar graph; Cycle;
    All these keywords.

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