Abstract
In this paper we provide exponential-time algorithms to enumerate the maximal irredundant sets of chordal graphs and two of their subclasses. We show that the maximum number of maximal irredundant sets of a chordal graph is at most \(1.7549^n\), and these can be enumerated in time \(O(1.7549^n)\). For interval graphs, we achieve the better upper bound of \(1.6957^n\) for the number of maximal irredundant sets and we show that they can be enumerated in time \(O(1.6957^n)\). Finally, we show that forests have at most \(1.6181^n\) maximal irredundant sets that can be enumerated in time \(O(1.6181^n)\). We complement the latter result by providing a family of forests having at least \(1.5292^n\) maximal irredundant sets.
This work is supported by the Research Council of Norway by the CLASSIS project and the French National Research Agency by the ANR project GraphEn (ANR-15-CE40-0009).
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Golovach, P.A., Kratsch, D., Liedloff, M., Sayadi, M.Y. (2017). Enumeration and Maximum Number of Maximal Irredundant Sets for Chordal Graphs. In: Bodlaender, H., Woeginger, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2017. Lecture Notes in Computer Science(), vol 10520. Springer, Cham. https://doi.org/10.1007/978-3-319-68705-6_22
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