On a possible extension of Hall's theorem to bipartite hypergraphs

Abstract In [1] an extension of Hall's theorem was conjectured for n -partite n -graphs and its fractional version was proved. It seems that the conjecture can be strengthened to apply any bipartite hypergraph (i.e. a hypergraph with a distinguished set of vertices A such that | e ∩ A | = 1 for every edge e ). We prove the strengthened conjecture in the case that | A |⩽4 and also give a proof for its fractional version.