Induced subgraphs and tree decompositions XIV. Non-adjacent neighbours in a hole
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913776993828864 |
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| author | Chudnovsky, Maria Hajebi, Sepehr Spirkl, Sophie |
| author_facet | Chudnovsky, Maria Hajebi, Sepehr Spirkl, Sophie |
| contents | A clock is a graph consisting of an induced cycle $C$ and a vertex not in $C$ with at least two non-adjacent neighbours in $C$. We show that every clock-free graph of large treewidth contains a "basic obstruction" of large treewidth as an induced subgraph: a complete graph, a subdivision of a wall, or the line graph of a subdivision of a wall. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05719 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Induced subgraphs and tree decompositions XIV. Non-adjacent neighbours in a hole Chudnovsky, Maria Hajebi, Sepehr Spirkl, Sophie Combinatorics A clock is a graph consisting of an induced cycle $C$ and a vertex not in $C$ with at least two non-adjacent neighbours in $C$. We show that every clock-free graph of large treewidth contains a "basic obstruction" of large treewidth as an induced subgraph: a complete graph, a subdivision of a wall, or the line graph of a subdivision of a wall. |
| title | Induced subgraphs and tree decompositions XIV. Non-adjacent neighbours in a hole |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2311.05719 |