Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911267658137600 |
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| author | Musin, Oleg R. |
| author_facet | Musin, Oleg R. |
| contents | Every graph G can be embedded in a Euclidean space as a two-distance set. This allows us to reformulate the analogue of Borsuk's conjecture for two-distance sets in terms of graphs. This conjecture remains open for dimensions from 4 to 63. This short note also discusses an approach for finding counterexamples using graphs, as well as its generalization for s-distance sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03668 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs Musin, Oleg R. Combinatorics Metric Geometry Every graph G can be embedded in a Euclidean space as a two-distance set. This allows us to reformulate the analogue of Borsuk's conjecture for two-distance sets in terms of graphs. This conjecture remains open for dimensions from 4 to 63. This short note also discusses an approach for finding counterexamples using graphs, as well as its generalization for s-distance sets. |
| title | Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2511.03668 |