On the diameter of cut polytopes - Archive ouverte HAL Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2013

On the diameter of cut polytopes

Résumé

Given an undirected graph G with node set V, the cut polytope is defined as the convex hull of the incidence vectors of all the cuts in G. And for a given integer k in the set {1,2,...,|V|-1}, the uniform cut polytope with parameter value k is defined as the convex hull of the cuts which correspond to a bipartition of the node set into sets with cardinalities k and |V|-k. In this paper, we study the diameter of these two families of polytopes. With respect to the cut polytope, we show a linear upper bound on its diameter (improving on one stemming from the reference: [F. Barahona and A.R. Mahjoub, On the cut polytope, Mathematical Programming 36, 157-173 (1986)]), give its value for trees and complete bipartite graphs. Then concerning uniform cut polytopes, we establish bounds on their diameter for different graph families, we provide some connections with other partition polytopes in the literature, and introduce sufficient and necessary conditions for adjacency on their 1-skeleton
Fichier principal
Vignette du fichier
manuscript.pdf (263.96 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01335919 , version 1 (22-06-2016)

Identifiants

  • HAL Id : hal-01335919 , version 1

Citer

José Neto. On the diameter of cut polytopes. [Research Report] Dépt. Réseaux et Service Multimédia Mobiles (Institut Mines-Télécom-Télécom SudParis); Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (Institut Mines-Télécom-Télécom SudParis-CNRS). 2013, pp.20. ⟨hal-01335919⟩
56 Consultations
61 Téléchargements

Partager

Gmail Facebook X LinkedIn More