I believe Minimum Dominating Set (MDS) is NP-hard for bounded degeneracy and their subset bounded degree graphs, but a paper appear to suggest tractability. Enumeration of Minimal Dominating Sets and Variants p.5
Proposition 1. Dom admits a polynomial delay algorithm when restricted to
Strongly chordal graphs.
Graph classes of bounded degeneracy.
The delay of the algorithm is the time between enumerating two MDSs after polynomial preprocessing (unless I have misunderstood the definitions on p. 3). According to graphclasses.org MDS is linear for strongly chordal graphs.
Does the paper imply $\exp(o(n))$ complexity of MDS for graphs of bounded degeneracy (and bounded degree)?