Gerry Toft

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20202025

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4 papers · 1 filter

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.CO2024

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…

math.CO2020

Trinets encode orchard phylogenetic networks

Charles Semple, Gerry Toft

Rooted triples, rooted binary phylogenetic trees on three leaves, are sufficient to encode rooted binary phylogenetic trees. That is, if $T$ and $T^{'}$ are rooted b…

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

Trinets encode orchard phylogenetic networks

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