Packing cliques in 3‐uniform hypergraphs

Abstract

For positive integers $n\geq k\geq t$ , a collection $B$ of $k$‐subsets of an $n$‐set is called a $t$‐packing if every $t$‐subset of $X$ appears in at most one set in $B$. In this paper, we investigate the existence of the maximum 3‐packings whenever $n$ is sufficiently larger than $k$. When $n \not\equiv 2 \ (mod \ k-2)$, the optimal value for the size of a 3‐packing is settled. In other cases, lower and upper bounds are obtained where mostly differ by an additive constant depending only on $k$ but one case that they differ by a linear bound in $n$.