Feige's Hypergraph Moore-Bound Conjecture
Statement
At the conjectured density, must every -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 .
Context
Feige's 2008 conjecture, well known in TCS with a substantial partial-results literature.
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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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