Planar graphs with distance of 3-cycles at least 2 and no cycles of lengths 5, 6, 7

Tao Wang, Ya-Nan Wang and Xiaojing Yang

Applied Mathematics and Computation, 2024, vol. 481, issue C

Abstract: Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to many graph coloring parameters. In this article, we prove that planar graphs with distance of 3-cycles at least 2 and no cycles of lengths 5,6,7 are weakly 2-degenerate. Furthermore, such graphs can be vertex-partitioned into two subgraphs, one of which has no edges, and the other is a forest.

Keywords: Weakly degenerate; (I,F)-partitionable; Planar graphs (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324004077

DOI: 10.1016/j.amc.2024.128946

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