Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs
Combinatorics
2025-11-18 v2 Metric Geometry
Abstract
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.
Cite
@article{arxiv.2511.03668,
title = {Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs},
author = {Oleg R. Musin},
journal= {arXiv preprint arXiv:2511.03668},
year = {2025}
}
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6 pages