Algorithms on graphs of bounded degeneracy/arboricity

There is one more approach to solve problems like Max Clique on graphs of bounded degeneracy.
You can look at the complement graph of a graph $G$ (i.e. every edge is a non-edge and every non-edge is an edge).
Solving Max Clique on $G$ is the same as solving Max Independent set on the complement.

For the complement of bounded degeneracy graphs algorithms for many problems are known.
E.g. Maximum Independent Set, Minimum Dominating Set, Perfect Code, k-Coloring, H-
Cover, H-Homomorphism and H-Role Assignment are FPT parameterized by the degeneracy of the complement.
See http://www.ii.uib.no/~martinv/Papers/Logarithmic_booleanwidth.pdf (submitted to journal)

Some of these problems make sense to translate to the complement graph, such as:

Can G be colored with $k$ colors -> can the complement be covered by $k$ cliques? (fixed $k$)

Is there an $3$-regular induced subgraph of $G$ -> is there an induced $k$ regular subgraph of the complement on $k+4$ vertices?