We show that for any positive integers g and t, there is a K6(1)-induced-minor-free graph of girth at least g that is not a region intersection graph over the class of Kt-minor-free graphs. This answers in a strong form the recently raised question of whether for every graph H there is a graph H′ such that H-induced-minor-free graphs are region intersection graphs over H′-minor-free graphs.
@article{arxiv.2504.21115,
title = {Induced Minors and Region Intersection Graphs},
author = {Édouard Bonnet and Robert Hickingbotham},
journal= {arXiv preprint arXiv:2504.21115},
year = {2025}
}