06030384

j

06030384 Brandst\"adt, Andreas Giakoumakis, Vassilis Maffray, Fr\'ed\'eric Clique separator decomposition of hole-free and diamond-free graphs and algorithmic consequences. Discrete Appl. Math. 160, No. 4-5, 471-478 (2012). 2012 Elsevier Science B.V. (North-Holland), Amsterdam EN clique separator decomposition hole-free and diamond-free graphs hole-free and paraglider-free graphs perfect graphs efficient algorithms

doi:10.1016/j.dam.2011.10.031

Summary: 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.