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International audience; A uniform cut polytope is defined as the convex hull of the incidence vectors of all cuts in an undirected graph G for which the cardinalities of the shores are fixed. In this paper, we study linear descriptions of such polytopes. Complete formulations are presented for the cases when the cardinality k of one side of the cut is equal to 1 or 2. For larger values of k, investigations with relation to the shape of these polytopes are reported. We namely determine their diameter and also provide new families of facet-defining inequalities

International audience; Given an undirected graph G, a uniform cut polytope is defined as the convex hull of the incidence vectors of the cuts in G for which the size of the shores are fixed. In this paper we show that simple extensions of facet-defining inequalities for the equipartition polytope introduced by Conforti et al. in [5] and [6] provide facet-defining inequalities for uniform cut polyhedra.

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

Given an undirected graph, a uniform cut polytope is defined as the convex hull of the incidence vectors of cuts for which the size of the shores are fixed. In this paper we show that simple extensions of facet defining inequalities for the equipartition polytope introduced by Conforti et al. provide facet defining inequalities for uniform cut polyhedra