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.
Jafarpour-Golzari, R. (2019). A generalization of Hall's theorem for $k$-uniform $k$-partite hypergraphs. Transactions on Combinatorics, 8(3), 25-30. doi: 10.22108/toc.2019.105022.1506
MLA
Jafarpour-Golzari, R. . "A generalization of Hall's theorem for $k$-uniform $k$-partite hypergraphs", Transactions on Combinatorics, 8, 3, 2019, 25-30. doi: 10.22108/toc.2019.105022.1506
HARVARD
Jafarpour-Golzari, R. (2019). 'A generalization of Hall's theorem for $k$-uniform $k$-partite hypergraphs', Transactions on Combinatorics, 8(3), pp. 25-30. doi: 10.22108/toc.2019.105022.1506
CHICAGO
R. Jafarpour-Golzari, "A generalization of Hall's theorem for $k$-uniform $k$-partite hypergraphs," Transactions on Combinatorics, 8 3 (2019): 25-30, doi: 10.22108/toc.2019.105022.1506
VANCOUVER
Jafarpour-Golzari, R. A generalization of Hall's theorem for $k$-uniform $k$-partite hypergraphs. Transactions on Combinatorics, 2019; 8(3): 25-30. doi: 10.22108/toc.2019.105022.1506
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