A Set and Collection Lemma

Details A Set and Collection Lemma A Set and Collection Lemma

2011-01-24

arxiv.org/abs/1101.4564v5

Computer Science

Discrete Mathematics

7 pages, 3 figures

Scientific paper

A set S is independent if no two vertices from S are adjacent. In this paper we prove that if F is a collection of maximum independent sets of a graph, then there is a matching from S-{intersection of all members of F} into {union of all members of F}-S, for every independent set S. Based on this finding we give alternative proofs for a number of well-known lemmata, as the "Maximum Stable Set Lemma" due to Claude Berge and the "Clique Collection Lemma" due to Andr\'as Hajnal.

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