Sensitivity and Hamming graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912983233331200 |
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| author | Asensio, Sara Filmus, Yuval García-Marco, Ignacio Knauer, Kolja |
| author_facet | Asensio, Sara Filmus, Yuval García-Marco, Ignacio Knauer, Kolja |
| contents | For any $m\geq 3$ we show that the Hamming graph $H(n,m)$ admits an imbalanced partition into $m$ sets, each inducing a subgraph of low maximum degree. This improves previous results by Tandya and by Potechin and Tsang, and disproves the Strong $m$-ary Sensitivity Conjecture of Asensio, García-Marco, and Knauer. On the other hand, we prove their weaker $m$-ary Sensitivity Conjecture by showing that the sensitivity of any $m$-ary function is bounded from below by a polynomial expression in its degree. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_08951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sensitivity and Hamming graphs Asensio, Sara Filmus, Yuval García-Marco, Ignacio Knauer, Kolja Combinatorics Computational Complexity For any $m\geq 3$ we show that the Hamming graph $H(n,m)$ admits an imbalanced partition into $m$ sets, each inducing a subgraph of low maximum degree. This improves previous results by Tandya and by Potechin and Tsang, and disproves the Strong $m$-ary Sensitivity Conjecture of Asensio, García-Marco, and Knauer. On the other hand, we prove their weaker $m$-ary Sensitivity Conjecture by showing that the sensitivity of any $m$-ary function is bounded from below by a polynomial expression in its degree. |
| title | Sensitivity and Hamming graphs |
| topic | Combinatorics Computational Complexity |
| url | https://arxiv.org/abs/2505.08951 |