Enumeration and maximum number of maximal irredundant sets for chordal graphs

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 an n-vertex chordal graph is at most 1.7549n, and these can be enumerated in time O(1.7549n). For interval graphs, we achieve the better upper bound of 1.6957n for the number of maximal irredundant sets and we show that they can be enumerated in time O(1.6957n). Finally, we show that an n-vertex forest has at most 1.6181n maximal irredundant sets that can be enumerated in time O(1.6181n). We complement the latter result by providing a family of forests having at least 1.5292n maximal irredundant sets.