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.

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Correspondence to Grigor Gasparyan*.

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* Visiting of the French Ministry of Research and Technology, laboratoire LEIBNIZ, Grenoble, November 1995—April 1996.

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Gasparyan*, G., Preissmann, M. & Sebő, A. Imperfect and Nonideal Clutters: A Common Approach. Combinatorica 23, 283–302 (2003).

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AMS Subject Classification (2000):

  • 05B40
  • 90C57
  • 90C10
  • 05C17
  • 05C15