  In this paper, we study several coloring problems on graphs from the
viewpoint of parameterized complexity. We show that Precoloring Extension is
fixed-parameter tractable (FPT) parameterized by distance to clique and
Equitable Coloring is FPT parameterized by the distance to threshold graphs. We
also study the List k-Coloring and show that the problem is NP-complete on
split graphs and it is FPT parameterized by solution size on split graphs.
