Abstract
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 language | English |
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Journal | Electronic Journal of Combinatorics |
Volume | 21 |
Issue number | 1 |
DOIs | |
State | Published - 28 Feb 2014 |
Keywords
- Clique
- Core
- Corona
- Independent set
- Matching
- Stable set