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arXiv · 2504.01233

The Borsuk Problem for Subsets of the Vertices of the 10-Dimensional Boolean Cube

Igor Batmanov·Vsevolod Voronov
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Abstract

In the papers Ziegler(2001) and Goldstein(2012) it was previously shown that any subset of the Boolean cube $ S \subset \{0,1\}^n $ for $ n \leq 9 $ can be partitioned into $n+1$ parts of smaller diameter, i.e., the Borsuk conjecture holds for such subsets. In this paper, it is shown that this is also true for $ n=10 $; however, the complexity of the computational verification increases significantly. In order to perform the computations in a reasonable time, several heuristics were developed to reduce the search tree. The SAT solver $\textbf{kissat}$ was used to cut off the search branches.

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Igor Batmanov, Vsevolod Voronov. 2025-04-01. The Borsuk Problem for Subsets of the Vertices of the 10-Dimensional Boolean Cube. https://arxiv.org/abs/2504.01233

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