W. Ge

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20242026

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math.CO2026

Degeneracy: From Graphs to Matroids

Allan Bickle, James Dylan Douthitt, Wayne Ge +1

A graph is $k$ -degenerate if every subgraph has a vertex of degree at most $k$ . We extend this notion to matroids, defining a loopless matroid $M$ to be $k$ -degenerate if every res…

math.CO2026

The Kővari-Sós-Turán theorem for $GF (q)$ -representable matroids

Wayne Ge

In this paper, we establish an analogue of the Kővari-Sós-Turán Theorem for $GF (q)$ -representable matroids. For $2 \leq s \leq t$ , we show that if $M$ is a rank- $n$ si…

math.CO2026

Unavoidable flats in connected regular matroids

Wayne Ge

This paper proves that every $2$ -connected regular matroid of sufficiently large rank has a $2$ -connected graphic flat of large rank. Furthermore, we explicitly determine a list of…

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…

Degeneracy: From Graphs to Matroids

The Kővari-Sós-Turán theorem for GF(q)-representable matroids

Unavoidable flats in connected regular matroids

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

Super-minimally 3-connected matroids

The Kővari-Sós-Turán theorem for $GF (q)$ -representable matroids

Super-minimally $3$ -connected matroids