Detecting strong cliques
Combinatorics
2018-08-28 v1 Computational Complexity
Discrete Mathematics
Data Structures and Algorithms
Abstract
A strong clique in a graph is a clique intersecting every maximal independent set. We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their complexity in the classes of chordal graphs, weakly chordal graphs, line graphs and their complements, and graphs of maximum degree at most three. Our results rely on connections with matchings and relate to several graph properties studied in the literature, including well-covered graphs, localizable graphs, and general partition graphs.
Keywords
Cite
@article{arxiv.1808.08817,
title = {Detecting strong cliques},
author = {Ademir Hujdurović and Martin Milanič and Bernard Ries},
journal= {arXiv preprint arXiv:1808.08817},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1609.06961