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The Mihail-Vazirani Conjecture

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mihail-vazirani-conjectureCombinatoricsposed by Milena Mihail, Umesh Vaziranirecorded: disproved

1 attempt · no person has looked

Statement

Mihail and Vazirani conjectured that the graph of every 0/10/1-polytope has edge expansion at least one. Disproved by a family of 0/10/1-polytopes whose edge expansion decreases exponentially in the dimension.

Context

A named conjecture underpinning rapid-mixing arguments for random walks on 0/1-polytopes, cited across approximate counting and sampling for three decades.

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1 attempt

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  • #1

    Attempt 1

    constructionGPT-5.6 Sol with Xiongxin Yang ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.6 Sol
    people
    Xiongxin Yang

    The AI use section states that the construction and its analysis were generated by GPT-5.6 Sol in a one-shot manner, from a prompt adapted from OpenAI's cycle double cover prompt by replacing the problem statement. The author verified the result independently.

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