Hujdurovic, Ademir Milanic, Martin Ries, Bernard 2019 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. application/pdf https://folia.unifr.ch/global/documents/307860 https://folia.unifr.ch/documents/307860/files/strongcliquesrero.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.disc.2019.06.010 info:eu-repo/semantics/openAccess License undefined Discrete Mathematics. - 2019, vol. 342, no. 9, p. 2738-2750 Strong clique Weakly chordal graph Line graph Cubic graph NP-hardness Polynomial-time algorithm info:eu-repo/classification/udc/004 Detecting strong cliques http://purl.org/coar/resource_type/c_6501