Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width

The linear maximum induced matching width (LMIM-width) of a graph is a width parameter based on the maximum induced matching in some of its subgraphs. In this paper we study output-polynomial enumeration algorithms on graphs of bounded LMIM-width and graphs of bounded local LMIM-width. In particular, we show that all 1-minimal \((\sigma ,\rho )\)-dominating sets, and hence all minimal dominating sets, of graphs of bounded LMIM-width can be enumerated with polynomial (linear) delay using polynomial space. Furthermore, we show that all minimal dominating sets of a unit square graph can be enumerated in incremental polynomial time.