The triangle closure is a polyhedron
نویسندگان
چکیده
منابع مشابه
The Triangle Closure is a Polyhedron
Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with certain families of lattice-free sets are polyhedra. For a long time, the only result known was the celebrated theorem of Cook, Kannan and Schrijver who showe...
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It is well-know that the Chvátal-Gomory (CG) closure of a rational polyhedron is a rational polyhedron. In this paper, we show that the CG closure of a bounded full-dimensional ellipsoid, described by rational data, is a rational polytope. To the best of our knowledge, this is the first extension of the polyhedrality of the CG closure to a nonpolyhedral set. A key feature of the proof is to ver...
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A famous theorem due to E. Steinitz states, in one of its formulations, that every planar (or, equivalently, every spherical) graph can be realized as the graph of edges and vertices of a convex polyhedron in Euclidean 3-space (see, for example, Grünbaum [1, Section 13.1] or Ziegler [3, Chapter 4]). This representation is possible in many different ways, but in all of them the circuits that bou...
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متن کاملThe General Triangle Is Unique
Some acute-angled triangles are special, e.g. right-angled or isosceles triangles. Some are not of this kind, but, without measuring angles, look as if they are. In that sense, there is exactly one general triangle. This well-known fact[1] is proven here formally.
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2013
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-013-0639-y