Crowns in linear \(3\)-graphs of minimum degree \(4\) (Q2094887)

Summary: A 3-graph is a pair \(H = (V, E)\) of sets, where elements of \(V\) are called points or vertices and \(E\) contains some 3-element subsets of \(V\), called edges. A 3-graph is called linear if any two distinct edges intersect in at most one vertex. There is a recent interest in extremal properties of 3-graphs containing no crown, three pairwise disjoint edges and a fourth edge which intersects all of them. We show that every linear 3-graph with minimum degree 4 contains a crown. This is not true if 4 is replaced by 3.