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On graphs admitting two disjoint maximum independent sets
(University of Primorska, 2023) Deniz, Zakir; Levit, V.E.; Mandrescu, E.
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. © 2022 Colegio Oficial de la Psicología de Madrid.