Solution of two fractional packing problems of Lovász

AbstractLovász asked whether the following is true for each hypergraph H and natural number k:(*) if νk(H′)=k·ν*(H′) holds for each hypergraph H′ arising from H by multiplication of points, then νk(H)=τk(H);(**) if τk(H′)=k·τ*(H′) holds for each hypergraph H′ arising from H by removing edges, then τk(H)=νk(H).We prove and generalize assertion (*) and give a counterexample to (**)