Critical and maximum independent sets of a graph

Adi Jarden, Vadim E. Levit, Eugen Mandrescu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let G be a simple graph with vertex set VG. A set A⊆VG is independent if no two vertices from A are adjacent. If αG+μG=|VG|, then G is called a König–Egerváry graph (Deming, 1979; Sterboul, 1979), where αG is the size of a maximum independent set and μG stands for the cardinality of a largest matching in G. The number dX=X−N(X) is the difference of X⊆VG, and a set A⊆VG is critical if d(A)=max{dX:X⊆VG} (Zhang, 1990). In this paper, we present various connections between unions and intersections of maximum and/or critical independent sets of a graph, which lead to new characterizations of König–Egerváry graphs.

Original languageEnglish
Pages (from-to)127-134
Number of pages8
JournalDiscrete Applied Mathematics
StatePublished - 1 Oct 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.


  • Core
  • Corona
  • Critical set
  • König–Egerváry graph
  • Maximum independent set


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