Erdős problem 775 · problems.science

Is there a $3$ -uniform hypergraph on $n$ vertices which contains at least $n-O(1)$ different sizes of cliques (maximal complete subgraphs)?

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FormalConjectures/ErdosProblems/

775.lean

Retained formal statement2 of 4

The answer is no, as proved by Gao [Ga25]: more generally, for any $k\geq 3$ , every $k$ -uniform hypergraph on $n$ vertices contains at most $n-f_k(n)$ different sizes of cliques, where $f_k(n)\to \infty$ as $n\to \infty$ .

FormalConjectures/ErdosProblems/775.leanErdos775.erdos_775.variants.gao3 linesExact file

1∃ f,2  Filter.Tendsto f Filter.atTop Filter.atTop ∧3    ∀ᶠ (n : ℕ) in Filter.atTop, ∀ (H : ThreeUniformHypergraph (Fin n)), H.cliqueSizes.ncard + f n ≤ n

SolvedStatement only, no proof

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