A sufficient condition for planar graphs with girth 5 to be (1,6)-colorable

Ganchao Zhang, Min Chen and Weifan Wang

Applied Mathematics and Computation, 2024, vol. 474, issue C

Abstract: A graph G is (d1,d2)-colorable if its vertices can be partitioned into two subsets V1 and V2 such that Δ(G[V1])≤d1 and Δ(G[V2])≤d2. Let G5 denote the family of planar graphs with girth at least 5. In this paper, we prove that every graph in G5 without adjacent 5-cycles is (1,6)-colorable.

Keywords: Improper coloring; Planar graphs; Cycle; Discharging method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:474:y:2024:i:c:s0096300324001784

DOI: 10.1016/j.amc.2024.128706

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