Enumerating Minimal Dominating Sets in Kt-free Graphs and Variants

Abstract

It is a long-standing open problem whether the minimal dominating sets of a graph can be enumerated in output-polynomial time. In this article we investigate this problem in graph classes defined by forbidding an induced subgraph. In particular, we provide output-polynomial time algorithms for Kt-free graphs and for several related graph classes. This answers a question of Kanté et al. about enumeration in bipartite graphs.