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

Andreas Brandstädt (1) , Vassilis Giakoumakis , Frédéric Maffray (2)

1 Fachbereich Informatik
2 G-SCOP_OC - Optimisation Combinatoire

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.

Domaines: Mathématique discrète [cs.DM]

Andreas Brandstädt, Vassilis Giakoumakis, Frédéric Maffray. Clique separator decomposition of hole-free and diamond-free graphs and algorithmic consequences. Discrete Applied Mathematics, 2012, 160 (4-5), pp.471-478. ⟨10.1016/j.dam.2011.10.031⟩. ⟨hal-00764257⟩