Domination is one of the classical subjects in structural graph theory and in graph algorithms. The Minimum Dominating Set problem and many of its variants are NP-complete and have been stud-ied from various algorithmic perspectives. One of those variants called irredundance is highly related to domination. For example, every min-imal dominating set of a graph G is also a maximal irredundant set of G. In this paper we study the enumeration of the maximal irredundant sets of a claw-free graph. We show that an n-vertex claw-free graph has O(1.9341n) maximal irredundant sets and these sets can be enumerated in the same time. We complement the aforementioned upper bound with a lower bound by providing a family of graphs having 1.5848nmaximal irredundant sets.
CITATION STYLE
Golovach, P. A., Kratsch, D., & Sayadi, M. Y. (2017). Enumeration of maximal irredundant sets for claw-free graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10236 LNCS, pp. 297–309). Springer Verlag. https://doi.org/10.1007/978-3-319-57586-5_25
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