منابع مشابه
Graphic vertices of the metric polytope
The metric polytope ,//~. is defined by the triangle inequalities: xij-Xik-Xjk <~ 0 and xii + Xik + Xjk ~< 2 for all triples i,j, k of(1 ..... n}. The integral vertices of ~¢¢~. are the incidence vectors of the cuts of the complete graph Kn. Therefore, ~¢~. is a relaxation of the cut polytope of K~. We study here the fractional vertices of ~¢¢~. Many of them are constructed from graphs; this is...
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We consider polyhedra with applications to well-know combinatorial optimization problems: the metric polytope mn and its relatives. For n ≤ 6 the description of the metric polytope is easy as mn has at most 544 vertices partitioned into 3 orbits; m7 the largest previously know instance has 275 840 vertices but only 13 orbits. Using its large symmetry group, we enumerate orbitwise 1 550 825 600 ...
متن کاملOn the Vertices of the d-Dimensional Birkhoff Polytope
Let us denote by Ωn the Birkhoff polytope of n× n doubly stochastic matrices. As the Birkhoff–von Neumann theorem famously states, the vertex set of Ωn coincides with the set of all n× n permutation matrices. Here we consider a higherdimensional analog of this basic fact. Let Ω n be the polytope which consists of all tristochastic arrays of order n. These are n×n×n arrays with nonnegative entri...
متن کاملThe number of vertices of a Fano polytope
The first part of this Theorem has been conjectured in [6] for any smooth Fano variety X, generalizing a conjecture by S. Mukai. Observe that after Mori theory, we always have ιX ≤ n+1 [13]; moreover ιX = n+1 if and only if X ∼= P [9]. For a smooth Fano variety X, (i) is known in the cases ιX ≥ 1 2 n+1 [20, 15], n ≤ 4 [6], n = 5 [2], and, provided that X admits an unsplit covering family of rat...
متن کامل*-graphs of Vertices of the Generalized Transitive Tournament Polytope
A nonnegative matrix T = (tij)~,j= 1 is a generalized transitive tournament matrix (GTT matrix) if tii = 0, t o = 1 tj~ for i # j , and 1 ~< t o + tjk + t~ ~< 2 for i, j , k pairwise distinct. The problem we are interested in is the characterization of the set of vertices of the polytope {GTT}n of all GTT matrices of order n. In 1992, Brualdi and Hwang introduced the *-graph associated to each ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00091-v