Document Type
Article
Publication Date
1-1-2022
Abstract
Halin proved that every minimally k-connected graph has a vertex of degree k. More generally, does every minimally vertically k-connected matroid have a k-element cocircuit? Results of Murty and Wong give an affirmative answer when k \leq 3. We show that every minimally vertically 4-connected matroid with at least six elements has a 4-element cocircuit, or a 5-element cocircuit that contains a triangle, with the exception of a specific nonbinary 9-element matroid. Consequently, every minimally vertically 4-connected binary matroid with at least six elements has a 4-element cocircuit.
Publication Source (Journal or Book title)
SIAM Journal on Discrete Mathematics
First Page
2822
Last Page
2829
Recommended Citation
Oxley, J., & Walsh, Z. (2022). SMALL COCIRCUITS IN MINIMALLY VERTICALLY 4-CONNECTED MATROIDS. SIAM Journal on Discrete Mathematics, 36 (4), 2822-2829. https://doi.org/10.1137/21M1454869