I was asked to construct a 4-uniform projective plane (meaning, a 4-uniform hypergraph that every two vertices belong to a single edge, and every two edges intersect in a single vertex).
I managed to construct the hypergraph below (each colored line is an edge). Now I am asked to find its $\nu^*$, which is the fractional matching number. The (not) fractional matching number is 1, since the maximum number of pairwise disjoint edges is 1.
Any ideas on how to find $\nu^*$? (without using MATLAB). Maybe it is related somehow to r-partite hypergraphs?
