W. Ge

activity

20242026

collaborators

10 papers

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…

math.CO2025

Reconstruction of C_4-free graphs from the set of closed neighborhoods and digital convexity

Steffen Borgwardt, MacKenzie Carr, Ce Chen +4

Fomin, Kratochvíl, Lokshtanov, Mancini, and Telle showed that every $C_{4}$ -free graph is reconstructible from the \emph{multiset} of closed neighborhoods. We strengthen their resu…

math.CO2025

Super-minimally $3$ -connected graphs

Wayne Ge

In this paper, we introduce super-minimally $k$ -connected graphs, those $k$ -connected graphs in which no proper subgraph is $k$ -connected. For $k$ greater than or equal to three, t…

math.CO2025

Rainbow triangles and the Erdős-Hajnal problem in projective geometries

Carolyn Chun, James Dylan Douthitt, Wayne Ge +3

We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs, in both its usual 'induced' form and the multicolou…

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.GR2024

The algebraic structure of hyperbolic graph braid groups

B. Appiah, P. Dani, W. Ge +8

Genevois recently classified which graph braid groups on $\geq 3$ strands are word hyperbolic. In the $3$ -strand case, he asked whether all such word hyperbolic groups are actually…

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

Reconstruction of C_4-free graphs from the set of closed neighborhoods and digital convexity

Super-minimally 3-connected graphs

Rainbow triangles and the Erdős-Hajnal problem in projective geometries

Unavoidable cycle-contraction minors of large 2-connected graphs

The algebraic structure of hyperbolic graph braid groups

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

Super-minimally $3$ -connected matroids

Super-minimally $3$ -connected graphs

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