A generalization of hall's theorem for k-uniform k-partite hypergraphs
Combinatorics
2016-10-04 v1
Abstract
In this paper we prove a generalized version of Hall's theorem for hypergraphs. More precisely, let H be a k-uniform k- partite hypergraph with some ordering on parts as V1, V2,..., Vk. such that the subhypergraph generated on union of V1, V2,..., Vk-1 has a unique perfect matching. In this case, we give a necessary and sufficient condition for having a matching of size t = |V1| in H. Some relevant results and counterexamples are given as well.
Keywords
Cite
@article{arxiv.1605.02972,
title = {A generalization of hall's theorem for k-uniform k-partite hypergraphs},
author = {Reza Jafarpour-Golzari},
journal= {arXiv preprint arXiv:1605.02972},
year = {2016}
}
Comments
7pages, 2 figures