  Graph editing problems offer an interesting perspective on sub- and
supergraph identification problems for a large variety of target properties.
They have also attracted significant attention in recent years, particularly in
the area of parameterized complexity as the problems have rich parameter
ecologies.
  In this paper we examine generalisations of the notion of editing a graph to
obtain a regular subgraph. In particular we extend the notion of regularity to
include two variants of edge-regularity along with the unifying constraint of
strong regularity. We present a number of results, with the central observation
that these problems retain the general complexity profile of their
regularity-based inspiration: when the number of edits $k$ and the maximum
degree $r$ are taken together as a combined parameter, the problems are
tractable (i.e. in \FPT{}), but are otherwise intractable.
  We also examine variants of the basic editing to obtain a regular subgraph
problem from the perspective of parameterizing by the treewidth of the input
graph. In this case the treewidth of the input graph essentially becomes a
limiting parameter on the natural $k+r$ parameterization.
