  We show that edge-clique graphs of cocktail party graphs have unbounded
rankwidth. This, and other observations lead us to conjecture that the
edge-clique cover problem is NP-complete for cographs. We show that the
independent set problem on edge-clique graphs of cographs. We show that the
independent set problem on edge-clique graphs of graphs without odd wheels
remains NP-complete. We present a PTAS for planar graphs and show that the
problem is polynomial for planar graphs without triangle separators.
