Clique separator decomposition of hole-free and diamond-free graphs and algorithmic consequences

Andreas Brandstädt, Vassilis Giakoumakis, Frédéric Maffray
2012 Discrete Applied Mathematics  
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