Jim Geelen

activity

20142026

most citedNaji's characterization of circle graphs

2 citations · 6 across the 7 of their papers we have counts for

collaborators

9 papers

math.CO2026

Unavoidable flats in GF(q)-representable matroids

Jim Geelen, Matthew E. Kroeker, Peter Nelson

We show that, for any finite field $F$ and positive integer $k$ , a simple $F$ -representable matroid $M$ with sufficiently high rank contains a rank- $k$ flat which…

math.CO2026

OpenAI's proof of the Cycle Double Cover Theorem

Jim Geelen

The following notes are my attempt to clarify, to myself, the OpenAI proof of the Cycle Double Cover Conjecture. This write-up offers no new insights, but some people may find it e…

math.CO2023

Average plane-size in complex-representable matroids

Rutger Campbell, Jim Geelen, Matthew E. Kroeker

Melchior's inequality implies that the average line-length in a simple, rank- $3$ , real-representable matroid is less than $3$ . A similar result holds for complex-representable matr…

math.CO2023

Unavoidable flats in matroids representable over prime fields

Jim Geelen, Matthew E. Kroeker

We show that, for any prime $p$ and integer $k \geq 2$ , a simple GF( $p$ )-representable matroid with sufficiently high rank has a rank- $k$ flat which is either independent in $M$ , o…

math.CO2018★ 2 cited

Naji's characterization of circle graphs

Jim Geelen, Edward Lee

We present a simpler proof of Naji's characterization of circle graphs.

math.CO2017

Improved bounds for Rota's Basis Conjecture

Sally Dong, Jim Geelen

We prove that, if $B_{1}, \dots, B_{n}$ are disjoint bases of a rank- $n$ matroid, then there are at least $⌊ \frac{n}{6 ⌈ l o g n ⌉} ⌋$ disjoint transversals of $(…

math.CO2015★ 2 cited

Quasi-graphic matroids

Jim Geelen, Bert Gerards, Geoff Whittle

Frame matroids and lifted-graphic matroids are two interesting generalizations of graphic matroids. Here we introduce a new generalization, {\em quasi-graphic matroids}, that unifi…

math.CO2015

Computing girth and cogirth in perturbed graphic matroids

Jim Geelen, Rohan Kapadia

We give polynomial-time randomized algorithms for computing the girth and the cogirth of binary matroids that are low-rank perturbations of graphic matroids.

math.CO2014★ 2 cited

Odd circuits in dense binary matroids

Jim Geelen, Peter Nelson

We show that, for each real number $α > 0$ and odd integer $k \geq 5$ there is an integer $c$ such that, if $M$ is a simple binary matroid with $∣ M ∣ \geq α 2^{r (M)}$ and with no $k$ -ele…