Notes on “Ideal 0, 1 matrices” by Cornuéjols and Novick

In 1994, Cornuéjols and Novick published a classification of ideal and minimally non-ideal circulant clutters. One of their main results for doing so relates contractions of these clutters, simple directed cycles in an appropriate graph, and algebraic conditions. The purpose of this paper is twofold: to correct a small inaccuracy of the necessity of the algebraic conditions in the original proof, and to show that these algebraic conditions are actually sufficient, by giving a constructive proof of the existence of cycles.