A note on the edge cover number and independence number in hypergraphs

Consider a hypergraph of rank r>2r>2 with mm edges, independence number αα and edge cover number ρρ. We prove the inequalityρ⩽(r-2)m+αr-1.One application of this inequality is a special case of a conjecture of Aharoni and the first author extending Ryser's Conjecture to matroids.