A short proof for the polyhedrality of the Chv 'atal-Gomory closure of a\n compact convex set

2012/07/20 by Gábor Braun, Sebastian Pokutta, Braun, Gábor +1
Computer Science · Mathematics · #90C05 #90C10 #90C25 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Complexity and Algorithms in Graphs #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1207.4884

openalex publication_date 2012/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently Schrijver's open problem, whether the Chv 'atal--Gomory closure of\nan irrational polytope is polyhedral was answered independently in the\naffirmative by Dadush, Dey, and Vielma (even for arbitrarily compact convex\nset) as well as by Dunkel and Schulz. We present a very short, easily accesible\nproof that the Chv 'atal--Gomory closure of a compact convex set is a polytope.\n

Related

• On the Chvatal-Gomory Closure of a Compact Convex Set
• On the Polyhedrality of the Chvatal-Gomory Closure
• On a generalization of the Chvatal-Gomory closure
• Counterexample to a conjecture of Ziegler concerning a simple polytope and its dual
• Notes on Convex Sets, Polytopes, Polyhedra, Combinatorial Topology, Voronoi Diagrams and Delaunay Triangulations