Title

On the intersections of circuits and cocircuits in matroids

Document Type

Article

Publication Date

6-1-1984

Abstract

Seymour has shown that a matroid has a triad, that is, a 3-element set which is the intersection of a circuit and a cocircuit, if and only if it is non-binary. In this paper we determine precisely when a matroid M has a quad, a 4-element set which is the intersection of a circuit and a cocircuit. We also show that this will occur if M has a circuit and a cocircuit meeting in more than four elements. In addition, we prove that if a 3-connected matroid has a quad, then every pair of elements is in a quad. The corresponding result for triads was proved by Seymour. © 1984 Akadémiai Kiadó.

Publication Source (Journal or Book title)

Combinatorica

First Page

187

Last Page

195

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