A P4 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 P4, the paw, or the diamond. This answers a~question of Dabrowski, Johnson, and Paulusma.
@article{arxiv.2605.15453,
title = {Clique-width and induced topological minors},
author = {Paweł Rafał Bieliński and Jadwiga Czyżewska and Martin Milanič and Amir Nikabadi and Paweł Rzążewski},
journal= {arXiv preprint arXiv:2605.15453},
year = {2026}
}