A new infinite family of 4-regular crossing-critical graphs

Zongpeng Ding; Yuanqiu Huang; Fengming Dong

A new infinite family of 4-regular crossing-critical graphs

Combinatorics 2024-04-16 v1

Authors: Zongpeng Ding , Yuanqiu Huang , Fengming Dong

Abstract

A graph $G$ is said to be crossing-critical if $cr(G-e)< cr(G)$ for every edge $e$ of $G$ , where $cr(G)$ is the crossing number of $G$ . Richter and Thomassen [Journal of Combinatorial Theory, Series B 58 (1993), 217-224] constructed an infinite family of 4-regular crossing-critical graphs with crossing number $3$ . In this article, we present a new infinite family of 4-regular crossing-critical graphs.

Keywords

crossing-critical graphs 4-regular graphs crossing number graph theory infinite family

Cite

@article{arxiv.2404.09434,
  title  = {A new infinite family of 4-regular crossing-critical graphs},
  author = {Zongpeng Ding and Yuanqiu Huang and Fengming Dong},
  journal= {arXiv preprint arXiv:2404.09434},
  year   = {2024}
}

Related papers

View all related →