Demonstrates the relation between quasi-isometry and path-width in graphs, implying that bounded path-width graphs can be weighted effectively.
We show that if a graph G admits a quasi-isometry $ϕ$ 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 $ϕ$ is a quasi-isometry to this weighted version of H, with error only an additive constant.
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Nguyen et al. (2025) studied this question.
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