1-Planar graphs with no 5-cycles are 5-degenerate

Qingqin Wu, Weifan Wang and Jiangxu Kong

Applied Mathematics and Computation, 2025, vol. 495, issue C

Abstract: A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is k-degenerate if each of its subgraphs contains a vertex of degree no greater than k. It was known that 1-planar graphs are 7-degenerate. In this paper, we show that every 1-planar graph without 5-cycles is 5-degenerate, which extends some known results on the 5-degeneracy of some 1-planar graphs.

Keywords: 1-Planar graph; Degeneracy; Cycle; Minimum degree (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000311

DOI: 10.1016/j.amc.2025.129304

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