Hadwiger's Conjecture for some graphs with independence number two
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911819721867264 |
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| author | Li, Tong Zhou, Qiang |
| author_facet | Li, Tong Zhou, Qiang |
| contents | Let $h(G)$ denote the largest $t$ such that $G$ contains $K_t$ as a minor and $χ(G)$ be the chromatic number of $G$ respectively. In 1943, Hadwiger conjectured that $h(G) \geq χ(G)$ for any graph $G$. In this paper, we prove that Hadwiger's conjecture holds for $H$-free graphs with independence number two, where $H$ is one of some specified graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05868 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hadwiger's Conjecture for some graphs with independence number two Li, Tong Zhou, Qiang Combinatorics Let $h(G)$ denote the largest $t$ such that $G$ contains $K_t$ as a minor and $χ(G)$ be the chromatic number of $G$ respectively. In 1943, Hadwiger conjectured that $h(G) \geq χ(G)$ for any graph $G$. In this paper, we prove that Hadwiger's conjecture holds for $H$-free graphs with independence number two, where $H$ is one of some specified graphs. |
| title | Hadwiger's Conjecture for some graphs with independence number two |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2305.05868 |