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1-Planar graphs without 6-cycles are 6-choosable

Year: 2026

Type: preprint

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 at most $k$. It was known that every 1-planar graph is 8-choosable. In this paper, we show that every 1-planar graph without 6-cycles is 5-degenerate and hence 6-choosable.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.23154

Authors: Wu, Qingqin, Wang, Yiqiao

Institutions: Zhejiang University of Finance and Economics, Beijing University of Technology

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G8631368005

OpenAlex ID: W7171511166

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