Induced subgraphs and tree decompositions XIX. Thetas and forests
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914378986553344 |
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| author | Chudnovsky, Maria Codsi, Julien Hajebi, Sepehr Spirkl, Sophie |
| author_facet | Chudnovsky, Maria Codsi, Julien Hajebi, Sepehr Spirkl, Sophie |
| contents | Let $H$ be a graph and let $\mathcal{C}$ be a hereditary class of theta-free graphs such that $H\notin \mathcal{C}$. We prove that if (a) $H$ is a forest; and (b) $\mathcal{C}$ excludes the line graphs of all subdivisions of some wall, then the treewidth of every graph in $\mathcal{C}$ is at most a polynomial function of its clique number. This is best possible in that both (a) and (b) are necessary for the existence of $any$ function with the above property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Induced subgraphs and tree decompositions XIX. Thetas and forests Chudnovsky, Maria Codsi, Julien Hajebi, Sepehr Spirkl, Sophie Combinatorics Let $H$ be a graph and let $\mathcal{C}$ be a hereditary class of theta-free graphs such that $H\notin \mathcal{C}$. We prove that if (a) $H$ is a forest; and (b) $\mathcal{C}$ excludes the line graphs of all subdivisions of some wall, then the treewidth of every graph in $\mathcal{C}$ is at most a polynomial function of its clique number. This is best possible in that both (a) and (b) are necessary for the existence of $any$ function with the above property. |
| title | Induced subgraphs and tree decompositions XIX. Thetas and forests |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.05602 |