Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.08277 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917900833521664 |
|---|---|
| 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 |