Abstract
An independent 2-clique of a graph is a subset of vertices that is an independent set and such that any two vertices inside have a common neighbor outside. In this paper, we study the complexity of finding an independent 2-clique of maximum size in several graph classes and we compare its complexity with the complexity of maximum independent set. We prove that this problem is NP-hard on apex graphs, APX-hard on line graphs, not \(n^{1/2-\epsilon }\)-approximable on bipartite graphs and not \(n^{1-\epsilon }\)-approximable on split graphs, while it is polynomial-time solvable on graphs of bounded degree and their complements, graphs of bounded treewidth, planar graphs, \((C_3,C_6)\)-free graphs, threshold graphs, interval graphs and cographs.
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Bazgan, C., Pontoizeau, T., Tuza, Z. (2017). On the Complexity of Finding a Potential Community. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_8
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DOI: https://doi.org/10.1007/978-3-319-57586-5_8
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