3 papers
math.CO2023
A binary-matroid analogue of a graph connectivity result of Jamison and Mulder
Cameron Crenshaw, James Oxley
Let be a graph such that, whenever two vertices and of are joined by three internally disjoint paths, and are adjacent. Jamison and Mulder determined that t…
math.CO2022
Ordering Circuits of Matroids
Cameron Crenshaw, James Oxley
The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adja…
math.CO2021
On the Cogirth of Binary Matroids
Cameron Crenshaw, James Oxley
The cogirth, , of a matroid is the size of a smallest cocircuit of . Finding the cogirth of a graphic matroid can be done in polynomial time, but Vardy showed in…