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
Recommended Citation
Oxley, J. (1984). On the intersections of circuits and cocircuits in matroids. Combinatorica, 4 (2-3), 187-195. https://doi.org/10.1007/BF02579220
