Lehman's forbidden minor characterization of ideal 0–1 matrices

✍ Scribed by Manfred Padberg

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 765 KB
• Volume: 111
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90178-v

✦ Synopsis

A zero-one matrix is ideal if its associated covering polyhedron is integral. In this note we document the proof of a lemma of A. Lehman that was communicated to us by U. Peled in 1979 and that characterizes square minimally nonideal zero-one matrices completely. We then give a somewhat different proof of a later (apparently, also unpublished) result of A. Lehman that was communicated to us by G. and that characterizes all minimally nonideal matrices completely. In particular, the proof given here, while based on Lehman's argument, does not utilize the width-length characterization of ideal matrices, also due to A. Lehman.