Hall's and Kőnig's theorem in graphs and hypergraphs

We investigate the relation between Hall's theorem and Kőnig's theorem in graphs and hypergraphs. In particular, we characterize the graphs satisfying a deficiency version of Hall's theorem, thereby showing that this class strictly contains all Kőnig-Egerváry graphs. Furthermore, we give a generalization of Hall's theorem to normal hypergraphs.