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List injective coloring of planar graphs

Author

Listed:
  • Cai, Jiansheng
  • Li, Wenwen
  • Cai, Wenjing
  • Dehmer, Matthias

Abstract

An injective coloring is a vertex coloring (not necessarily proper) such that any two vertices sharing a common neighbor receive distinct colors. A graph G is called injectively k-choosable, if for any color list L with admissible colors on V(G) of size k, there is an injective coloring φ such that φ(v)∈L(v) whenever v∈V(G). The list injective chromatic number, denoted by χil(G), is the least k for which G is injectively k-choosable. We focus on the study of list injective coloring on planar graphs which has disjoint 5−-cycles and show that χil(G)≤Δ+3 if Δ≥18 and χil(G)≤Δ+4 if Δ≥12.

Suggested Citation

  • Cai, Jiansheng & Li, Wenwen & Cai, Wenjing & Dehmer, Matthias, 2023. "List injective coloring of planar graphs," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    • Handle: RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006932
    DOI: 10.1016/j.amc.2022.127631
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    References listed on IDEAS

    as
    1. Min Chen & Geňa Hahn & André Raspaud & Weifan Wang, 2012. "Some results on the injective chromatic number of graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 299-318, October.
    2. Huijuan Wang & Bin Liu & Xin Zhang & Lidong Wu & Weili Wu & Hongwei Gao, 2016. "List edge and list total coloring of planar graphs with maximum degree 8," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 188-197, July.
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