On graphs admitting two disjoint maximum independent sets

Zakir Deniz, Vadim E. Levit, Eugen Mandrescu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


An independent set S is maximal if it is not a proper subset of an independent set, while S is maximum if it has a maximum size. The problem of whether a graph has a pair of disjoint maximal independent sets was introduced by Berge in the early 1970s. The class of graphs for which every induced subgraph admits two disjoint maximal independent sets was characterized by Schaudt in 2015. In this paper, we are focused on finding conditions ensuring the existence of two disjoint maximum independent sets.

Original languageEnglish
Article numberP1.01
JournalArt of Discrete and Applied Mathematics
Issue number1
StatePublished - 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 Colegio Oficial de la Psicología de Madrid.


  • König-Egervàry graph
  • Maximum independent set
  • almost bipartite graph
  • shedding vertex
  • unicyclic graph


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