Induced Minors and Region Intersection Graphs

Overview & Synopsis

We show that for any positive integers g and t, there is a K(1) 6 -induced-minor-free graph of girth at least g that is not a region intersection graph over the class of K tminor-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.