Pivot-minors and the Erdős-Hajnal conjecture
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
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| _version_ | 1866908306198495232 |
|---|---|
| author | Davies, James |
| author_facet | Davies, James |
| contents | We prove a conjecture of Kim and Oum that every proper pivot-minor-closed class of graphs has the strong Erdős-Hajnal property. More precisely, for every graph $H$, there exists $ε> 0$ such that every $n$-vertex graph with no pivot-minor isomorphic to $H$ contains two sets $A, B$ of vertices such that $|A|, |B| \ge εn$ and $A$ is complete or anticomplete to $B$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09133 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pivot-minors and the Erdős-Hajnal conjecture Davies, James Combinatorics We prove a conjecture of Kim and Oum that every proper pivot-minor-closed class of graphs has the strong Erdős-Hajnal property. More precisely, for every graph $H$, there exists $ε> 0$ such that every $n$-vertex graph with no pivot-minor isomorphic to $H$ contains two sets $A, B$ of vertices such that $|A|, |B| \ge εn$ and $A$ is complete or anticomplete to $B$. |
| title | Pivot-minors and the Erdős-Hajnal conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2305.09133 |