hypergraph is an assignment of a weight to each hyperedge such that the sum of weights near each vertex is at most one. The largest size of a fractional matching in a hypergraph H is denoted by . A fractional transversal in a hypergraph is an assignment of a weight to each vertex such that the sum of weights in each hyperedge is at least one. The smallest size of a fractional transversal in a hypergraph H is denoted by . Linear programming duality implies that . Furedi has proved the following fractional version of Ryser's conjecture: If H is r-partite and r-regular (each vertex appears in exactly r hyperedges), then.Lovasz has shown that. References Graph theory Hypergraphs