LAUSR

The matching number $$\alpha '(H)$$α′(H) of a hypergraph H is the size of a largest matching in H, where a matching is a set of pairwise disjoint edges in H. A dominating set in H is a subset D of vertices of H such that for every $$v\in V(H)\setminus D$$v∈V(H)\D there exists $$u\in D$$u∈D such that u and v lie in an edge of H, and the domination number of H, denoted by $$\gamma (H)$$γ(H), is the minimum cardinality of a dominating set in H. It was shown that a Ryser-like inequality $$\gamma (H)\le (r-1)\alpha '(H)$$γ(H)≤(r-1)α′(H) holds for hypergraphs H of rank r. In particular, for intersecting hypergraphs H of rank r, $$\gamma (H)\le r-1$$γ(H)≤r-1, since $$\alpha '(H)=1$$α′(H)=1. The linear intersecting hypergraphs of rank $$2\le r\le 4$$2≤r≤4 achieving the equality $$\gamma (H)=r-1$$γ(H)=r-1 have been characterized. In this paper we show that all the 5-uniform linear intersecting hypergraphs H with equality $$\gamma (H)=r-1$$γ(H)=r-1 are generated by the finite projective plane of order three.