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arXiv · 2605.15453

Clique-width and induced topological minors

Paweł Rafał Bieliński·Jadwiga Czyżewska·Martin Milanič·Amir Nikabadi·Paweł Rzążewski
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Abstract

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.

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Paweł Rafał Bieliński, Jadwiga Czyżewska, Martin Milanič, Amir Nikabadi, Paweł Rzążewski. 2026-05-14. Clique-width and induced topological minors. https://arxiv.org/abs/2605.15453

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