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arXiv · 2511.03668

Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs

Oleg R. Musin
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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.

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Oleg R. Musin. 2025-11-15. Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs. https://arxiv.org/abs/2511.03668

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