Gerry Toft

collaborators

3 papers

math.CO2025

A new minor-closed class of transversal matroids

Gerry Toft

We provide a characterisation of when a single-element contraction of a transversal matroid is itself transversal. Using this characterisation, we define a new class of transversal…

math.CO2025

The excluded minors of the class of spike minors

Sam Bastida, Nick Brettell, Rutger Campbell +4

Mayhew et al.\ (2021) posed the problem of showing that the minor-closed class of spikes and their minors has a finite set of excluded minors and describing all of them. In this pa…

math.CO2025

Detachable pairs in $3$ -connected matroids and simple $3$ -connected graphs

Nick Brettell, Charles Semple, Gerry Toft

Let $M$ be a $3$ -connected matroid. A pair ${e, f}$ in $M$ is detachable if $M \ e \ f$ or $M / e / f$ is $3$ -connected. Williams (2015) proved that if $M$ has a…

A new minor-closed class of transversal matroids

The excluded minors of the class of spike minors

Detachable pairs in 3-connected matroids and simple 3-connected graphs

Detachable pairs in $3$ -connected matroids and simple $3$ -connected graphs