An asymptotic resolution of a conjecture of Szemerédi and Petruska

André E. Kézdy, Jenő Lehel

Consider a $3$-uniform hypergraph of order $n$ with clique number $k$ such that the intersection of all its $k$-cliques is empty. Szemerédi and Petruska proved $n\le 8m^2+3m$, for…