A tree version of Konig's theorem
组合数学
2007-05-23 v2
摘要
Konig's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalisation of this result, in which each point in one side of the graph is replaced by a subtree of a given tree. The proof uses a recent extension of Hall's theorem to families of hypergraphs, by the first author and P. Haxell.
引用
@article{arxiv.math/9912134,
title = {A tree version of Konig's theorem},
author = {Ron Aharoni and Eli Berger and Ran Ziv},
journal= {arXiv preprint arXiv:math/9912134},
year = {2007}
}
备注
6 pages, no figures. Submitted to Combinatorica. Minor mistakes in the proofs in v1 were corrected