Alon, Seymour, and Thomas [J. Amer. Math. Soc. 1990] famously showed that every n-vertex Kh-minor-free graph has treewidth Oh(n). Recently, Distel, Dujmovi\'c, Eppstein, Hickingbotham, Joret, Micek, Morin, Seweryn, and Wood [SIAM J. Discrete Math. 2024] refined this by showing that these graphs are Oh(n)-blowups of treewidth 4 graphs. We improve this by showing that these graphs are Oh(n)-blowups of treewidth 3 graphs.
@article{arxiv.2510.09063,
title = {Graphs Excluding a Minor in Blowups of Treewidth 3 Graphs},
author = {Marc Distel},
journal= {arXiv preprint arXiv:2510.09063},
year = {2025}
}