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Clique separator decomposition, introduced by Whitesides and Tarjan, is one of the most important graph decompositions. A hole is a chordless cycle with at least five vertices. A paraglider is a graph with five vertices a, b, c, d, e and edges ab, ac, bc, bd, cd, ae, de. We show that every (hole, paraglider)-free graph admits a clique separator decomposition into graphs of three very specific types. This yields efficient algorithms for various optimization problems in this class of graphs.doi:10.1016/j.dam.2011.10.031 fatcat:226muztrbfhyzgchj5i2q3y6xi