A set and collection lemma

Vadim E. Levit, Eugen Mandrescu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


A set S⊆V(G) is independent if no two vertices from S are adjacent. Let α(G) stand for the cardinality of a largest independent set. In this paper we prove that if Λ is a nonempty collection of maximum independent sets of a graph G, and S is an independent set, then there is a matching from S-∩Λ into ∪Λ-S, and |S|+α(G) ≤ |{∩} Λ ∩S| + |∪Λ∪S|. Based on these findings we provide alternative proofs for a number of well-known lemmata, such as the "Maximum Stable Set Lemma" due to Claude Berge and the "Clique Collection Lemma" due to András Hajnal.

Original languageEnglish
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - 28 Feb 2014


  • Clique
  • Core
  • Corona
  • Independent set
  • Matching
  • Stable set


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