# 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