Tree-independence number VII. Excluding a star

Maria Chudnovsky; Jadwiga Czyżewska; Marcin Pilipczuk; Paweł Rzążewski

Tree-independence number VII. Excluding a star

Combinatorics 2026-01-01 v1

Authors: Maria Chudnovsky , Jadwiga Czyżewska , Marcin Pilipczuk , Paweł Rzążewski

Abstract

We prove that for every fixed integer $s$ and every planar graph $H$ , the class of $H$ -induced-minor-free and $K_{1,s}$ -induced-subgraph-free graphs has polylogarithmic tree-independence number. This is a weakening of a conjecture of Dallard, Krnc, Kwon, Milani\v{c}, Munaro, \v{S}torgel, and Wiederrecht.

Keywords

graph theory

Cite

@article{arxiv.2512.23887,
  title  = {Tree-independence number VII. Excluding a star},
  author = {Maria Chudnovsky and Jadwiga Czyżewska and Marcin Pilipczuk and Paweł Rzążewski},
  journal= {arXiv preprint arXiv:2512.23887},
  year   = {2026}
}

Related papers

View all related →