Tree-independence number VII. Excluding a star

TL;DR

This paper proves that certain classes of planar graphs excluding specific induced minors and subgraphs have a polylogarithmic tree-independence number, advancing understanding of graph structure constraints.

Contribution

It establishes that for fixed s and planar graphs H, the class of graphs excluding H-induced minors and K_{1,s}-induced subgraphs has polylogarithmic tree-independence number, weakening a prior conjecture.

Findings

Polylogarithmic tree-independence number for specified graph classes

Weakening of a conjecture by Dallard et al.

Extension to all fixed integers s and planar graphs H

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.