Tree-independence number VIII. 3PC-free graphs have logarithmic tree-independence number

Maria Chudnovsky; Julien Codsi; Ajaykrishnan E S; Daniel Lokshtanov; Ilya Maier

paper

Tree-independence number VIII. 3PC-free graphs have logarithmic tree-independence number

arXiv:2610.28865

Abstract

A three-path-configuration is a graph consisting of three pairwise internally vertex-disjoint paths, the union of every two of which is an induced cycle of length at least four. A graph is 3PC-free if no induced subgraph of it is a three-path-configuration. We show that 3PC-free graphs have logarithmic tree-independence number, which is asymptotically best possible.