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Main Authors: Chudnovsky, Maria, Cizma, Daniel, Linial, Nati
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2501.08277
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author Chudnovsky, Maria
Cizma, Daniel
Linial, Nati
author_facet Chudnovsky, Maria
Cizma, Daniel
Linial, Nati
contents A consistent path system in a graph $G$ is an collection of paths, with exactly one path between any two vertices in $G$. A path system is said to be consistent if it is intersection-closed. We say that $G$ is strictly metrizable if every consistent path system in $G$ can be realized as the system of unique geodesics with respect to some assignment of positive edge weight. In this paper, we show that the family of strictly metrizable graphs is minor-closed.
format Preprint
id arxiv_https___arxiv_org_abs_2501_08277
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Strictly Metrizable Graphs are Minor-Closed
Chudnovsky, Maria
Cizma, Daniel
Linial, Nati
Combinatorics
A consistent path system in a graph $G$ is an collection of paths, with exactly one path between any two vertices in $G$. A path system is said to be consistent if it is intersection-closed. We say that $G$ is strictly metrizable if every consistent path system in $G$ can be realized as the system of unique geodesics with respect to some assignment of positive edge weight. In this paper, we show that the family of strictly metrizable graphs is minor-closed.
title Strictly Metrizable Graphs are Minor-Closed
topic Combinatorics
url https://arxiv.org/abs/2501.08277