Enumerating minimal dominating sets in $K_t$-free graphs and variants

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