Solution of two fractional packing problems of Lovász Original Research Article

Lovász asked whether the following is true for each hypergraph H and natural number k: (image) if image holds for each hypergraph image arising from H by multiplication of points, then image; (image) if image holds for each hypergraph image arising from H by removing edges, then image. We prove and generalize assertion (image) and give a counterexample to (image).