The Borsuk Problem for Subsets of the Vertices of the 10-Dimensional Boolean Cube
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908295956004864 |
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| author | Batmanov, Igor Voronov, Vsevolod |
| author_facet | Batmanov, Igor Voronov, Vsevolod |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_01233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Borsuk Problem for Subsets of the Vertices of the 10-Dimensional Boolean Cube Batmanov, Igor Voronov, Vsevolod Combinatorics 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. |
| title | The Borsuk Problem for Subsets of the Vertices of the 10-Dimensional Boolean Cube |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.01233 |