On the domination number of a graph defined by containment

Abstract

Let $n>k>2$ be integers. Define a bipartite graph between all $k$-element and all $2$-element subsets of an $n$-element set by drawing an edge if and only if the first one contains the second. The domination number of this graph is determined up to a factor of $1+o\left(1\right)$. The short proof relies on some extremal results concerning hypergraphs.