Reverse Chv\'atal-Gomory rank
  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. 
Michele Conforti, Alberto Del Pia, Marco Di Summa, Yuri Faenza, and   Roland Grappe
math.OC math.CO math.MG