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A Boundary Property for Upper Domination

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9843)

Abstract

An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard, but can be solved in polynomial time in some restricted graph classes, such as \(P_4\)-free graphs or \(2K_2\)-free graphs. For classes defined by finitely many forbidden induced subgraphs, the boundary separating difficult instances of the problem from polynomially solvable ones consists of the so called boundary classes. However, none of such classes has been identified so far for the upper dominating set problem. In the present paper, we discover the first boundary class for this problem.

V. Lozin—The author gratefully acknowledges support from EPSRC, grant EP/L020408/1.

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Correspondence to Vadim Lozin .

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AbouEisha, H., Hussain, S., Lozin, V., Monnot, J., Ries, B., Zamaraev, V. (2016). A Boundary Property for Upper Domination. In: Mäkinen, V., Puglisi, S., Salmela, L. (eds) Combinatorial Algorithms. IWOCA 2016. Lecture Notes in Computer Science(), vol 9843. Springer, Cham. https://doi.org/10.1007/978-3-319-44543-4_18

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  • DOI: https://doi.org/10.1007/978-3-319-44543-4_18

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