Two more characterizations of König–Egerváry graphs

Adi Jarden, Vadim E. Levit, Eugen Mandrescu

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let G be a simple graph with vertex set V(G). A set S⊆V(G) is independent if no two vertices from S are adjacent. The graph G is known to be König–Egerváry if α(G)+μ(G)=|V(G)|, where α(G) denotes the size of a maximum independent set and μ(G) is the cardinality of a maximum matching. A nonempty collection Γ of maximum independent sets is König–Egerváry if |⋃Γ|+|⋂Γ|=2α(G) (Jarden et al., 2015). In this paper, we prove that G is a König–Egerváry graph if and only if for every two maximum independent sets S1,S2 of G, there is a matching from V(G)−S1∪S2 into S1∩S2. Moreover, the same is true, when instead of two sets S1 and S2 we consider an arbitrary König–Egerváry collection.

Original languageEnglish
Pages (from-to)175-180
Number of pages6
JournalDiscrete Applied Mathematics
Volume231
DOIs
StatePublished - 20 Nov 2017

Keywords

  • Core
  • Corona
  • König–Egerváry collection
  • König–Egerváry graph
  • Maximum independent set
  • Maximum matching

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