A new infinite family of 4-regular crossing-critical graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917639451836416 |
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| author | Ding, Zongpeng Huang, Yuanqiu Dong, Fengming |
| author_facet | Ding, Zongpeng Huang, Yuanqiu Dong, Fengming |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_09434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new infinite family of 4-regular crossing-critical graphs Ding, Zongpeng Huang, Yuanqiu Dong, Fengming Combinatorics 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. |
| title | A new infinite family of 4-regular crossing-critical graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.09434 |