Imperfect and Nonideal Clutters: A Common Approach

We prove three theorems. First, Lovász’s theorem about minimal imperfect clutters, including also Padberg’s corollaries. Second, Lehman’s result on minimal nonideal clutters. Third, a common generalization of these two. The endeavor of working out a ‘common denominator’ for Lovász’s and Lehman’s theorems leads, besides the common generalization, to a better understanding and simple polyhedral proofs of both.