English

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

R2 v1 2026-07-01T08:23:28.312Z