On cliques in hypergraphs

Abstract

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

6 pages, 1 figure, Erdős Problem #775, add a remark for $k=3$