Clique-width and induced topological minors
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911687593951232 |
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| author | Bieliński, Paweł Rafał Czyżewska, Jadwiga Milanič, Martin Nikabadi, Amir Rzążewski, Paweł |
| author_facet | Bieliński, Paweł Rafał Czyżewska, Jadwiga Milanič, Martin Nikabadi, Amir Rzążewski, Paweł |
| contents | A $P_4$ is a chordless path on four vertices. A diamond is a graph obtained from a clique of size four by removing one edge of the clique. A paw is a graph obtained from a clique of size four by removing two adjacent edges of the clique. We prove that for a graph $H$, the class of graphs with no induced subdivision of $H$ has bounded clique-width if and only if $H$ is an induced subgraph of $P_4$, the paw, or the diamond. This answers a~question of Dabrowski, Johnson, and Paulusma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15453 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Clique-width and induced topological minors Bieliński, Paweł Rafał Czyżewska, Jadwiga Milanič, Martin Nikabadi, Amir Rzążewski, Paweł Discrete Mathematics Combinatorics A $P_4$ is a chordless path on four vertices. A diamond is a graph obtained from a clique of size four by removing one edge of the clique. A paw is a graph obtained from a clique of size four by removing two adjacent edges of the clique. We prove that for a graph $H$, the class of graphs with no induced subdivision of $H$ has bounded clique-width if and only if $H$ is an induced subgraph of $P_4$, the paw, or the diamond. This answers a~question of Dabrowski, Johnson, and Paulusma. |
| title | Clique-width and induced topological minors |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2605.15453 |