Abstract
In this paper we prove a generalized version of Hall's theorem in graphs, for hypergraphs. More precisely, let $mathcal{H}$ be a $k$-uniform $k$-partite hypergraph with some ordering on parts as $V_{1}, V_{2},ldots,V_{k}$ such that the subhypergraph generated on $bigcup_{i=1}^{k-1}V_{i}$ has a unique perfect matching. In this case, we give a necessary and sufficient condition for having a matching of size $t=|V_{1}|$ in $mathcal{H}$. Some relevant results and counterexamples are given as well.
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