On the edge expansion of random polytopes

Asaf Ferber; Michael Krivelevich; Marcelo Sales; Wojciech Samotij

doi:10.1137/1.9781611978971.111

On the edge expansion of random polytopes

Asaf Ferber^*
, Michael Krivelevich
, Marcelo Sales^*
, Wojciech Samotij

^*Corresponding author for this work

School of Mathematical Sciences

University of California at Irvine

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A 0/1-polytope in ℝⁿ is the convex hull of a subset of {0,1}ⁿ. The graph of a polytope P is the graph whose vertices are the zero-dimensional faces of P and whose edges are the one-dimensional faces of P. A conjecture of Mihail and Vazirani states that the edge expansion of the graph of every 0/1-polytope is at least one. We study a random version of the problem, where the polytope is generated by selecting vertices of {0,1}ⁿ independently at random with probability p ∈ (0,1). Improving earlier results, we show that, for any p ∈ (0,1), with high probability the edge expansion of the random 0/1-polytope is bounded from below by an absolute constant.

Original language	English
Title of host publication	Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026
Editors	Kasper Green Larsen, Barna Saha
Publisher	Association for Computing Machinery
Pages	3022-3035
Number of pages	14
ISBN (Electronic)	9781611978971
DOIs	https://doi.org/10.1137/1.9781611978971.111
State	Published - 2026
Event	37th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026 - Vancouver, Canada Duration: 11 Jan 2026 → 14 Jan 2026

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume	2026-January
ISSN (Print)	1071-9040
ISSN (Electronic)	1557-9468

Conference

Conference	37th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026
Country/Territory	Canada
City	Vancouver
Period	11/01/26 → 14/01/26

Funding

Funders	Funder number
National Science Foundation
United States National Science Foundation
Israel Science Foundation	2110/22
Engineering Research Centers	101044123
United States-Israel Binational Science Foundation	2023688

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10.1137/1.9781611978971.111

Cite this

Ferber, A., Krivelevich, M., Sales, M., & Samotij, W. (2026). On the edge expansion of random polytopes. In K. G. Larsen, & B. Saha (Eds.), Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026 (pp. 3022-3035). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2026-January). Association for Computing Machinery. https://doi.org/10.1137/1.9781611978971.111

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title = "On the edge expansion of random polytopes",

abstract = "A 0/1-polytope in ℝn is the convex hull of a subset of \{0,1\}n. The graph of a polytope P is the graph whose vertices are the zero-dimensional faces of P and whose edges are the one-dimensional faces of P. A conjecture of Mihail and Vazirani states that the edge expansion of the graph of every 0/1-polytope is at least one. We study a random version of the problem, where the polytope is generated by selecting vertices of \{0,1\}n independently at random with probability p ∈ (0,1). Improving earlier results, we show that, for any p ∈ (0,1), with high probability the edge expansion of the random 0/1-polytope is bounded from below by an absolute constant.",

author = "Asaf Ferber and Michael Krivelevich and Marcelo Sales and Wojciech Samotij",

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doi = "10.1137/1.9781611978971.111",

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Ferber, A, Krivelevich, M, Sales, M & Samotij, W 2026, On the edge expansion of random polytopes. in KG Larsen & B Saha (eds), Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2026-January, Association for Computing Machinery, pp. 3022-3035, 37th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026, Vancouver, Canada, 11/01/26. https://doi.org/10.1137/1.9781611978971.111

On the edge expansion of random polytopes. / Ferber, Asaf; Krivelevich, Michael; Sales, Marcelo et al.
Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026. ed. / Kasper Green Larsen; Barna Saha. Association for Computing Machinery, 2026. p. 3022-3035 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2026-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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On the edge expansion of random polytopes

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