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arXiv · 2404.09434

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

Zongpeng Ding·Yuanqiu Huang·Fengming Dong
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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.

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Zongpeng Ding, Yuanqiu Huang, Fengming Dong. 2024-04-15. A new infinite family of 4-regular crossing-critical graphs. https://arxiv.org/abs/2404.09434

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