On Critical Circuits in k-Connected Matroids
Document Type
Article
Publication Date
11-1-2018
Abstract
We show that, for every integer k≥ 4 , if M is a k-connected matroid and C is a circuit of M such that for every e∈ C, M\ e is not k-connected, then C meets a cocircuit of size at most 2 k- 3 ; furthermore, if M is binary and k≥ 5 , then C meets a cocircuit of size at most 2 k- 4. It follows from our results and a result of Reid et al [5] that every minimally k-connected matroid has a cocircuit of size at most 2 k- 3 , and every minimally k-connected binary matroid has a cocircuit of size at most 2 k- 4.
Repository Citation
Costalonga, J.,
Deng, K.,
& Zhou, X.
(2018). On Critical Circuits in k-Connected Matroids. Graphs and Combinatorics, 34 (6), 1589-1595.
https://corescholar.libraries.wright.edu/math/385
DOI
10.1007/s00373-018-1974-9
