Document Type
Lecture
Publication Date
11-8-2023
Abstract
Spikes (also called tipless spikes in the matroid theory literature) form a well-known class of matroids that are important in the study of matroid connectivity. These matroids have the property that every pair of elements is contained in both a 4-element circuit and a 4-element cocircuit. We will present a family of generalizations of spikes, which we call (s, t)-spikes, with the property that every s-element subset of the ground set is contained in a 2s-element circuit and every t-element subset of the ground set is contained in a 2t-element cocircuit. We call this property the (s,2s,t,2t)-property. Our main result is that all sufficiently large matroids with the (s,2s,t,2t)-property are (s,t)-spikes. This is joint work with Nick Brettell.
Relational Format
presentation
Recommended Citation
Grace, Kevin, "Some generalizations of the class of spikes" (2023). Combinatorics Seminar. 13.
https://egrove.olemiss.edu/math_combinatorics/13
