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arXiv · 2510.14804

On cliques in hypergraphs

Jun Gao
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Abstract

We prove that for any $k \ge 3$, every $k$-uniform hypergraph on $n$ vertices contains at most $n - ω(1)$ different sizes of cliques (maximal complete subgraphs). In particular, the 3-uniform case answers a question of Erdős.

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Jun Gao. 2025-10-31. On cliques in hypergraphs. https://arxiv.org/abs/2510.14804

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