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A generalization of Hall's theorem for $k$-uniform $k$-partite hypergraphs | ||
| Transactions on Combinatorics | ||
| مقاله 12، دوره 8، شماره 3، آذر 2019، صفحه 25-30 اصل مقاله (426.51 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2019.105022.1506 | ||
| نویسنده | ||
| Reza Jafarpour-Golzari* | ||
| Department of Mathematics, Institute for Advanced Studies in Basic Science (IASBS), Zanjan, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| $k$-uniform $k$-partite hypergraph؛ matching؛ perfect matching؛ vertex cover؛ Hall's theorem | ||
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آمار تعداد مشاهده مقاله: 363 تعداد دریافت فایل اصل مقاله: 510 |
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