A tree version of Konig's theorem

Details A tree version of Konig's theorem A tree version of Konig's theorem

1999-12-16

arxiv.org/abs/math/9912134v2

Mathematics

Combinatorics

6 pages, no figures. Submitted to Combinatorica. Minor mistakes in the proofs in v1 were corrected

Scientific paper

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.

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