Induced subgraph density. VII. The five-vertex path
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866915812443422720 |
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| author | Nguyen, Tung Scott, Alex Seymour, Paul |
| author_facet | Nguyen, Tung Scott, Alex Seymour, Paul |
| contents | We prove the Erdős-Hajnal conjecture for the five-vertex path $P_5$; that is, there exists $c>0$ such that every $n$-vertex graph with no induced $P_5$ has a clique or stable set of size at least $n^c$. This completes the verification of the Erdős-Hajnal property of all five-vertex graphs. Our methods combine probabilistic and structural ideas with the iterative sparsification framework introduced in the third and fourth papers in the series. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_15333 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Induced subgraph density. VII. The five-vertex path Nguyen, Tung Scott, Alex Seymour, Paul Combinatorics We prove the Erdős-Hajnal conjecture for the five-vertex path $P_5$; that is, there exists $c>0$ such that every $n$-vertex graph with no induced $P_5$ has a clique or stable set of size at least $n^c$. This completes the verification of the Erdős-Hajnal property of all five-vertex graphs. Our methods combine probabilistic and structural ideas with the iterative sparsification framework introduced in the third and fourth papers in the series. |
| title | Induced subgraph density. VII. The five-vertex path |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.15333 |