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. 
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On representation of subsets

  • P. Hall
  • J. London Math. Sot
  • 1935

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