K2,3-induced minor-free graphs admit quasi-isometry with additive distortion to graphs of tree-width at most two

A graph H is an induced minor of a graph G if H can be obtained from G by a sequence of edge contractions and vertex deletions. Otherwise, G is H-induced minor-free. In this paper, we prove that K2,3-induced minor-free graphs admit a quasi-isometry with additive distortion to graphs with tree-width at most two. Our result implies that a recent conjecture of Nguyen et al. [Coarse tree-width (2025)] holds for K2,3-induced minor-free graphs.