Quasi-isometries between graphs with variable edge lengths
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929751632904192 |
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| author | Davies, James Hatzel, Meike Hickingbotham, Robert |
| author_facet | Davies, James Hatzel, Meike Hickingbotham, Robert |
| contents | This paper investigates quasi-isometries between graphs with variable edge lengths. A quasi-isometry is a mapping between metric spaces that approximately preserves distances, allowing for a bounded amount of additive and multiplicative distortion. Recently, Nguyen, Scott, and Seymour conjectured that, by appropriately adjusting the edge lengths of the target graph along with modifying the additive distortion constant, the multiplicative distortion factor could be eliminated. We disprove this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-isometries between graphs with variable edge lengths Davies, James Hatzel, Meike Hickingbotham, Robert Combinatorics Metric Geometry This paper investigates quasi-isometries between graphs with variable edge lengths. A quasi-isometry is a mapping between metric spaces that approximately preserves distances, allowing for a bounded amount of additive and multiplicative distortion. Recently, Nguyen, Scott, and Seymour conjectured that, by appropriately adjusting the edge lengths of the target graph along with modifying the additive distortion constant, the multiplicative distortion factor could be eliminated. We disprove this conjecture. |
| title | Quasi-isometries between graphs with variable edge lengths |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2503.07448 |