  The linear induced matching width (LMIM-width) of a graph is a width
parameter defined by using the notion of branch-decompositions of a set
function on ternary trees. 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 and all 1-maximal
(\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.
