English

Reverse Chv\'atal-Gomory rank

Optimization and Control 2014-09-29 v3 Combinatorics Metric Geometry

Abstract

We introduce the reverse Chv\'atal-Gomory rank r*(P) of an integral polyhedron P, defined as the supremum of the Chv\'atal-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.

Keywords

Cite

@article{arxiv.1211.0388,
  title  = {Reverse Chv\'atal-Gomory rank},
  author = {Michele Conforti and Alberto Del Pia and Marco Di Summa and Yuri Faenza and Roland Grappe},
  journal= {arXiv preprint arXiv:1211.0388},
  year   = {2014}
}

Comments

21 pages, 4 figures

R2 v1 2026-06-21T22:32:00.356Z