We introduce a way to associate a family of circuits to an arbitrary clutter, suggested by a theorem of Lehman. Several characterizations of matroid ports using their circuits are presented. แฎ 1997 Academic Press 0 0 0 ลฝ . component of M that contains e , then P M, e is completely unaffected 0 0 by
Clutters and Circuits, II
โ Scribed by Lorenzo Traldi
- Book ID
- 102558703
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 285 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0196-8858
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โฆ Synopsis
We continue to study ways of defining circuits associated with clutters, and we give several new characterizations of matroid ports using their circuits. We also discuss the use of these circuits to analyze redundancies among elements appearing in nonmatroidal reliability problems.
๐ SIMILAR VOLUMES
A map on clutters (collections of incomparable sets of a given set) is a function defined from the class of all clutters to itself, that sends a clutter on a ground set E to a clutter on the same set. Here we study two maps on clutters, the blocker map and the complementary map. Our main results in
A clutter is k-monotone, completely monotone or threshold if the corresponding Boolean function is k-monotone, completely monotone or threshold, respectively. A characterization of k-monotone clutters in terms ofexcluded minors is presented here. This result is used to derive a characterization of 2
## Motivated by Lehman's characterization of the minor-minimal clutters without the MFMC property, we propose a conjecture about the minor-minimal clutters with tlr< kq where k>2 is a fixed integer. We prove, without using Lehman's theorem, this conjecture for the case k=2. We introduce diadic clu