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On list r-hued coloring of outer-1-planar graphs

Author

Listed:
  • Liang, Lingmei
  • Liu, Fengxia
  • Lai, Hong-Jian

Abstract

Let L be list assignment of colors available for vertices of a graph G, an (L,r)-coloring of G is a proper coloring c such that for any vertex v∈V(G), we have c(v)∈L(v) and |c(N(v))|≥min{d(v),r}. The r-hued list chromatic number of G, denoted as χL,r(G), is the least integer k, such that for list assignment L satisfying |L(v)|=k∀v∈V(G), G has an (L,r)-coloring. A graph G is an outer-1-planar graph if G has a drawing on the plane such that all vertices of V(G) are located on the outer face of this drawing, and each edge can cross at most one other edge. For any positive integer r, we completely determine the upper bound of list r-hued chromatic number for all outer-1-planar graphs. This extended a former result in [Discrete Mathematics and Theoretical Computer Science, 23:3 (2021)].

Suggested Citation

  • Liang, Lingmei & Liu, Fengxia & Lai, Hong-Jian, 2023. "On list r-hued coloring of outer-1-planar graphs," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007299
    DOI: 10.1016/j.amc.2022.127658
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    References listed on IDEAS

    as
    1. Chen, Ye & Fan, Suohai & Lai, Hong-Jian & Song, Huimin & Xu, Murong, 2020. "Decomposition and r-hued Coloring of K4(7)-minor free graphs," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    2. Huang, Danjun & Wang, Yiqiao & Lv, Jing & Yang, Yanping & Wang, Weifan, 2019. "List coloring and diagonal coloring for plane graphs of diameter two," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    3. Xin Zhang, 2017. "Total coloring of outer-1-planar graphs with near-independent crossings," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 661-675, October.
    4. Dailly, Antoine & Duchêne, Éric & Parreau, Aline & Sidorowicz, Elżbieta, 2022. "The neighbour sum distinguishing relaxed edge colouring," Applied Mathematics and Computation, Elsevier, vol. 419(C).
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