论文信息 - Polytope des independants d'un graphe serie-parallele

Polytope des independants d'un graphe serie-parallele

A graph is said to be serie-parallel if it doesn't contain an homeomorph to K"4. The aim of the paper is the demonstration of Chvatal's conjecture on the polytope of independent set of vertices in such graphs. This is done classically by using LP-duality, the algorithm for constructing the primal-dual solution having the nice property to be linear in the number of vertices.

Mouloud Boulala | Jean-Pierre Uhry | Mouloud Boulala | J. Uhry

[1] V. Chvátal. On certain polytopes associated with graphs , 1975 .

[2] Leslie E. Trotter,et al. A class of facet producing graphs for vertex packing polyhedra , 1975, Discret. Math..

[3] L. A. Wolsey,et al. Further facet generating procedures for vertex packing polytopes , 1976, Math. Program..

[4] Vasek Chvátal,et al. Edmonds polytopes and a hierarchy of combinatorial problems , 1973, Discret. Math..

[5] M. Padberg. On the Complexity of Set Packing Polyhedra , 1977 .

[6] Leslie E. Trotter,et al. Properties of vertex packing and independence system polyhedra , 1974, Math. Program..

[7] Uri N. Peled. Properties of Facets of Binary Polytopes , 1977 .

[8] A. Tucker,et al. The Strong Perfect Graph Conjecture for Planar Graphs , 1973, Canadian Journal of Mathematics.

[9] R. Duffin. Topology of series-parallel networks , 1965 .

[10] Leslie E. Trotter,et al. Vertex packings: Structural properties and algorithms , 1975, Math. Program..

[11] Najiba Sbihi,et al. Algorithme de recherche d'un stable de cardinalite maximum dans un graphe sans etoile , 1980, Discret. Math..

[12] Manfred W. Padberg,et al. On the facial structure of set packing polyhedra , 1973, Math. Program..