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

@article{Aharoni1990OnAP,
title={On a possible extension of Hall's theorem to bipartite hypergraphs},
author={Ron Aharoni and Ofra Kessler},
journal={Discrete Mathematics},
year={1990},
volume={84},
pages={309-313}
}

In [l] 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 to any bipartite hypergraph (i.e. a hypergraph with a distinguished set of vertices A such that ]e r7Al = 1 for every edge e). We prove the strengthened conjecture in the case that IAl S 4 and also give a proof for its fractional version.