We prove that the tree independence number of every even-hole-free graph is at most polylogarithmic in its number of vertices. More explicitly, we prove that there exists a constant c>0 such that for every integer n>1 every n-vertex even-hole-free graph has a tree decomposition where each bag has stability (independence) number at most c log^10 n. This implies that the Maximum Weight Independent Set problem, as well as several other natural algorithmic problems that are known to be NP-hard in general, can be solved in quasi-polynomial time if the input graph is even-hole-free.
@article{arxiv.2407.08927,
title = {Tree Independence Number IV. Even-hole-free Graphs},
author = {Maria Chudnovsky and Peter Gartland and Sepehr Hajebi and Daniel Lokshtanov and Sophie Spirkl},
journal= {arXiv preprint arXiv:2407.08927},
year = {2024}
}