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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.05602 |
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Table of 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.