Dominated balanced separators in wheel-induced-minor-free graphs
Combinatorics
2025-12-16 v1 Discrete Mathematics
Abstract
Gartland and Lokshtanov conjectured that every graph that excludes some planar graph as an induced minor has a balanced separator, that is, a separator whose deletion leaves every component with no more than half of the vertices of the graph, which is dominated by a bounded number of vertices. We confirm this conjecture for excluding any fixed wheel, that is, a cycle together with a universal vertex, as an induced minor.
Keywords
Cite
@article{arxiv.2512.12329,
title = {Dominated balanced separators in wheel-induced-minor-free graphs},
author = {Maria Chudnovsky and J. Pascal Gollin and Matjaž Krnc and Martin Milanič},
journal= {arXiv preprint arXiv:2512.12329},
year = {2025}
}
Comments
21 pages, 4 figures