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Feige's Hypergraph Moore-Bound Conjecture

Combinatorics · posed by Uriel Feige, 2008 · solved

1 attempt

Statement

At the conjectured density, must every kk-uniform hypergraph contain a short nontrivial even cover - a set of hyperedges covering each vertex an even number of times - with no superfluous polylogarithmic factors? Known up to polylog factors since 2022; now proved exactly for every k3k \ge 3.

Context

Feige's 2008 conjecture, well known in TCS with a substantial partial-results literature.

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.6 Sol, GPT-5.5 Pro, Claude Opus 4.8, Claude Fable 5 ·
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    GPT-5.6 Sol, GPT-5.5 Pro, Claude Opus 4.8, Claude Fable 5

    The colored-walk polynomial-interpolation argument over Kikuchi graphs was developed across several frontier models and written up by a five-author team, with an independent spectral proof alongside.

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