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Paper detail

A Set and Collection Lemma

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 András Hajnal.

preprint2011arXivOpen access
Vadim E. LevitEugen Mandrescu
math.CODiscrete Mathematics
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Vadim E. LevitEugen Mandrescu

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