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 statement3 of 4

For graphs, Spencer [Sp71] constructed a graph which contains cliques of at least $n-\log_2n+O(1)$ different sizes, which Moon and Moser [MoMo65] showed to be best possible.

FormalConjectures/ErdosProblems/775.leanErdos775.erdos_775.variants.moon_moser1 lineExact file

1∃ C, ∀ (n : ℕ) (G : SimpleGraph (Fin n)), ↑G.cliqueSizes.ncard ≤ ↑n - Real.logb 2 ↑n + C

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