Reverse Chvátal-Gomory Rank

We introduce the reverse Chvatal-Gomory rankr*(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)=+∞. 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. We also sketch possible extensions, in particular to the reverse split rank.

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