List injective coloring of planar graphs

Jiansheng Cai, Wenwen Li, Wenjing Cai and Matthias Dehmer

Applied Mathematics and Computation, 2023, vol. 439, issue C

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.

Keywords: Plane graphs; List injective coloring; Disjoint 5−-cycles; Maximum degree (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006932

DOI: 10.1016/j.amc.2022.127631

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