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

Qingqin Wu; Yiqiao Wang

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

Combinatorics 2026-07-25 v1

Authors: Qingqin Wu , Yiqiao Wang

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.

Cite

@article{arxiv.2607.23154,
  title  = {1-Planar graphs without 6-cycles are 6-choosable},
  author = {Qingqin Wu and Yiqiao Wang},
  journal= {arXiv preprint arXiv:2607.23154},
  year   = {2026}
}