Edge-clique graphs of cocktail parties have unbounded rankwidth
  In an attempt to find a polynomial-time algorithm for the edge-clique cover problem on cographs we tried to prove that the edge-clique graphs of cographs have bounded rankwidth. However, this is not the case. In this note we show that the edge-clique graphs of cocktail party graphs have unbounded rankwidth. 
Maw-Shang Chang and Ton Kloks and Ching-Hao Liu
cs.DM math.CO