On Ryser's conjecture for linear intersecting multipartite hypergraphs

We also report a number of computational results. For r=7, we find that there is no linear intersecting hypergraph that achieves the equality τ=r−1 in Ryser's conjecture, although non-linear examples are known. We exhibit intersecting non-linear examples achieving equality for r∈{9,13,17}. Also, we find that r=8 is the smallest value of r for which there exists a linear intersecting r-partite hypergraph that achieves τ=r−1 and is not isomorphic to a subhypergraph of a projective plane.