Computing the clique number of a-perfect graphs in polynomial time
PÊCHER, Arnaud
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
WAGLER, Annegret K.
Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes [LIMOS]
Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes [LIMOS]
PÊCHER, Arnaud
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Reformulations based algorithms for Combinatorial Optimization [Realopt]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
WAGLER, Annegret K.
Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes [LIMOS]
< Reduce
Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes [LIMOS]
Language
en
Article de revue
This item was published in
European Journal of Combinatorics. 2014, vol. 35, p. 449-458
Elsevier
English Abstract
A main result of combinatorial optimization is that the clique and chromatic numbers of a perfect graph are computable in polynomial time (Grotschel et al., 1981) [7]. This result relies on polyhedral characterizations of ...Read more >
A main result of combinatorial optimization is that the clique and chromatic numbers of a perfect graph are computable in polynomial time (Grotschel et al., 1981) [7]. This result relies on polyhedral characterizations of perfect graphs involving the stable set polytope of the graph, a linear relaxation defined by clique constraints, and a semi-definite relaxation, the Theta-body of the graph.A natural question is whether the algorithmic results for perfect graphs can be extended to graph classes with similar polyhedral properties. We consider a superclass of perfect graphs, the a-perfect graphs, whose stable set polytope is given by constraints associated with generalized cliques. We show that for such graphs the clique number can be computed in polynomial time as well. The result strongly relies upon Fulkerson's antiblocking theory for polyhedra and Lovasz's Theta function.Read less <
Origin
Hal imported