2012/11/02 by Michele Conforti, Alberto Del Pia, Conforti, Michele +7
Computer Science · Mathematics · #52B20 #52C07 #90C10 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Computational Geometry and Mesh Generation #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC) #math.CO #math.MG #math.OC #msc:52B20 #msc:52C07 #msc:90C10
paper · pdf · doi:10.48550/arxiv.1211.0388
21 pages, 4 figures
openalex publication_date 2012/11/02 · arxiv created 2014/09/26 · arxiv updated 2014/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the reverse Chvátal-Gomory rank r*(P) of an integral polyhedron P, defined as the supremum of the Chvátal-Gomory ranks of all rational polyhedra whose integer hull is P. A well-known example in dimension two shows that there exist integral polytopes P with r*(P) equal to infinity. We provide a geometric characterization of polyhedra with this property in general dimension, and investigate upper bounds on r*(P) when this value is finite.