Asymptotic structure. II. Path-width and additive quasi-isometry

Abstract

We show that if a graph $G$ admits a quasi-isometry $\ddot{I}•$ to a graph $H$ of bounded path-width, then we can assign a non-negative integer length to each edge of $H$, such that the same function $\ddot{I}•$ is a quasi-isometry to this weighted version of $H$, with error only an additive constant.

arXiv admin note: text overlap with arXiv:2501.09839