Journal article

Reverse Chvatal-Gomory Rank

We introduce the reverse Chvatal-Gomory rank r*(P) of an integral polyhedron P, defined as the supremum of the Chvatal-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) = +infinity. We provide a geometric characterization of polyhedra with this property in every dimension, and investigate upper bounds on r*(P) when this value is finite.


Related material