James G. Oxley

collaborators

4 papers

math.CO2026

The connected binary matroids with a pair of elements in no non-spanning circuits

Wayne Ge, James Oxley, Jagdeep Singh

Let $M$ be a simple connected binary matroid, and let $e$ and $f$ be distinct elements of $M$ . It is well known that, when the only circuits containing $e$ are spanning, $M$ is a c…

math.CO2026

Super-minimally $3$ -connected matroids

Wayne Ge, James Oxley

A super-minimally $k$ -connected matroid is a $k$ -connected matroid having no proper $k$ -connected restriction of size at least $2 k - 2$ . This extends the corresponding concept for gr…

math.CO2025

Unavoidable cycle-contraction minors of large $2$ -connected graphs

Wayne Ge, James Oxley

It is well known that every sufficiently large connected graph has, as an induced subgraph, $K_{n}$ , $K_{1, n}$ , or an $n$ -vertex path. A 2023 paper of Allred, Ding, and Oporowski ide…

math.CO2025

What is a 4-connected matroid?

Nick Brettell, Susan Jowett, James Oxley +2

The {\em breadth} of a tangle $T$ in a matroid is the size of the largest spanning uniform submatroid of the tangle matroid of $T$ . A matroid $M$ is {\em weakly…

The connected binary matroids with a pair of elements in no non-spanning circuits

Super-minimally 3-connected matroids

Unavoidable cycle-contraction minors of large 2-connected graphs

What is a 4-connected matroid?

Super-minimally $3$ -connected matroids

Unavoidable cycle-contraction minors of large $2$ -connected graphs