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arXiv · 1101.4564

A Set and Collection Lemma

Vadim E. Levit·Eugen Mandrescu
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Abstract

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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Vadim E. Levit, Eugen Mandrescu. 2011-01-24. A Set and Collection Lemma. https://arxiv.org/abs/1101.4564

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