Nguyen–Scott–Seymour conjecture on additive quasi-isometries to bounded-tree-width graphs

A graph is quasi-isometric to another graph if there is a quasi-isometry between their metric spaces; a quasi-isometry with additive distortion has bounded additive error in distances. The tree-width of a graph is the minimum width of a tree-decomposition of the graph.

Nguyen–Scott–Seymour conjecture. There is a constant $k$ such that if a graph $G$ admits a quasi-isometry to a graph of tree-width at most two, then $G$ admits a quasi-isometry with additive distortion to a graph of tree-width at most $k$.

This conjecture asks whether quasi-isometry to graphs of tree-width two can always be improved to a quasi-isometry with only additive distortion while retaining bounded tree-width. The supplied context presents it as a conjecture and does not state a resolution.