Strictly Metrizable Graphs are Minor-Closed
Combinatorics
2025-01-24 v2
Abstract
A consistent path system in a graph is an collection of paths, with exactly one path between any two vertices in . A path system is said to be consistent if it is intersection-closed. We say that is strictly metrizable if every consistent path system in 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.
Cite
@article{arxiv.2501.08277,
title = {Strictly Metrizable Graphs are Minor-Closed},
author = {Maria Chudnovsky and Daniel Cizma and Nati Linial},
journal= {arXiv preprint arXiv:2501.08277},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2311.09364