Independent sets in edge-clique graphs

We first show that the independent set problem on edge-clique graphs of cographs can be solved in O(n2) time. We then show that the independent set problem on edge-clique graphs of graphs without odd wheels is NP-complete. We present a PTAS for planar graphs and show that the problem is polynomial for planar graphs without triangle separators. Lastly, we show that edge-clique graphs of cocktail party graphs have unbounded rankwidth.