Chordality of clutters with vertex decomposable dual and ascent of clutters

Graphical representations of clutters

We discuss the use of K-terminal networks to represent arbitrary clutters. A given clutter has many di¤erent representations, and there does not seem to be any set of simple transformations that can be used to transform one representation of a clutter into any other. We observe that for t 2 the class of clutters that can be represented using no more than t terminals is closed under minors, and ...

Ideal clutters

From Clutters to Matroids

This paper deals with the question of completing a monotone increasing family of subsets Γ of a finite set Ω to obtain the dependent sets of a matroid. Specifically, we provide several natural processes for transforming the clutter Λ of the inclusionminimal subsets of the family Γ into the set of circuits C(M) of a matroid M with ground set Ω. In addition, by combining these processes, we prove...

Monotone clutters

Ding, G., Monotone clutters, Discrete Mathematics 119 (1993) 67-77. 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-monotone matroids and of 3-m...

Linearly dependent vectorial decomposition of clutters

This paper deals with the question of completing a monotone increasing family of subsets Γ of a finite set Ω to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we demonstrate that such vectorial completions of the family of subsets Γ exist and, in addition, we show that the minimal vectorial completions of the family Γ provide a decomposition of the...