Random 0/1-polytopes expand rapidly
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917399072079872 |
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| author | Guo, He Tomon, István |
| author_facet | Guo, He Tomon, István |
| contents | A 0/1-polytope is the convex hull of a subset $V\subseteq \{0,1\}^n$. A celebrated conjecture of Mihail and Vazirani asserts that the graph of every 0/1-polytope has edge-expansion at least 1. In this paper, we show that typical 0/1-polytopes have significantly stronger expansion. Specifically, if $V$ is formed by sampling each vertex of $\{0,1\}^n$ independently with constant probability $p$, then with high probability the edge-expansion is $Θ(n)$ for $p \in (1/2, 1)$, and $n^{Θ(\log \log n)}$ for $p \in (0, 1/2)$. This improves the previously best known bound $Ω(1)$ due to Ferber, Krivelevich, Sales and Samotij. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random 0/1-polytopes expand rapidly Guo, He Tomon, István Combinatorics Discrete Mathematics Probability A 0/1-polytope is the convex hull of a subset $V\subseteq \{0,1\}^n$. A celebrated conjecture of Mihail and Vazirani asserts that the graph of every 0/1-polytope has edge-expansion at least 1. In this paper, we show that typical 0/1-polytopes have significantly stronger expansion. Specifically, if $V$ is formed by sampling each vertex of $\{0,1\}^n$ independently with constant probability $p$, then with high probability the edge-expansion is $Θ(n)$ for $p \in (1/2, 1)$, and $n^{Θ(\log \log n)}$ for $p \in (0, 1/2)$. This improves the previously best known bound $Ω(1)$ due to Ferber, Krivelevich, Sales and Samotij. |
| title | Random 0/1-polytopes expand rapidly |
| topic | Combinatorics Discrete Mathematics Probability |
| url | https://arxiv.org/abs/2604.09520 |