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Problems / combinatorics

combinatorics / Polyhedral combinatorics

The Mihail-Vazirani Conjecture

Mihail and Vazirani conjectured that the graph of every $0/1$-polytope has edge expansion at least one. Disproved by a family of $0/1$-polytopes whose edge expansion decreases exponentially in the dimension.

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combinatoricsAug 3, 2026Significance 30/100Registry: unreviewed

The Mihail-Vazirani Conjecture

Prior state unknown→disproved

Mihail and Vazirani conjectured that the graph of every $0/1$-polytope has edge expansion at least one. Disproved by a family of $0/1$-polytopes whose edge expansion decreases exponentially in the dimension.

Source authenticatedThe Mihail-Vazirani Conjecture →
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Mihail and Vazirani conjectured that the graph of every $0/1$-polytope has edge expansion at least one. Disproved by a family of $0/1$-polytopes whose edge expansion decreases exponentially in the dimension.

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