On graphs admitting two disjoint maximum independent sets
Combinatorics
2019-02-01 v2 Discrete Mathematics
Abstract
An independent set A is maximal if it is not a proper subset of an independent set, while A 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 C. Berge in early 70's. The class of graphs for which every induced subgraph admits two disjoint maximal independent sets was characterized in (Shaudt, 2015). It is known that deciding whether a graph has two disjoint maximal independent sets is a NP-complete problem (Henning et al., 2009). In this paper, we are focused on finding conditions ensuring the existence of two disjoint maximum independent sets.
Keywords
Cite
@article{arxiv.1807.06914,
title = {On graphs admitting two disjoint maximum independent sets},
author = {Zakir Deniz and Vadim E. Levit and Eugen Mandrescu},
journal= {arXiv preprint arXiv:1807.06914},
year = {2019}
}
Comments
12 pages, 4 figures