Graph minors and metric spaces - Georgakopoulos, A; Papazoglou, P (Springer, 2025)
We present problems and results that combine graph-minors and coarse geometry. For example, we ask whether every geodesic metric space (or graph) without a fat H minor is quasi-isometric to a graph with no H minor, for an arbitrary finite graph H. We answer this affirmatively for a few small H. We also present a metric analogue of Menger’s theorem and König’s ray theorem. We conjecture metric analogues of the Erdös–Pósa Theorem and Halin’s grid theorem.