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

TL;DR

This paper presents output-polynomial algorithms for enumerating minimal dominating sets in $K_t$-free graphs, addressing a long-standing open problem and extending results to bipartite graph variants.

Contribution

It provides the first output-polynomial algorithms for enumeration in $K_t$-free graphs and their variants, solving a notable open problem.

Findings

Output-polynomial enumeration algorithms for $K_t$-free graphs.

Extension of enumeration algorithms to bipartite graph variants.

Resolution of a question posed by Kanté et al. regarding bipartite graphs.

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 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 Kant\'e et al. about enumeration in bipartite graphs.