3 papers
math.CO2026
The excluded minors for -gainable and regular biased graphs
Nick Brettell, Rutger Campbell, Daryl Funk +1
We prove that a biased graph is gainable over the group if and only if it contains no minor isomorphic to , , or . We develo…
math.CO2026
Myhill-Nerode for hypergraphs and an application to gain-graphic matroids
Daryl Funk, Angus Matthews, Dillon Mayhew
We present a Myhill-Nerode theorem for hypergraphs. The theorem involves an operation which takes two input structures and produces a hypergraph as output. Using this operation, we…
math.CO2025
Describing Quasi-Graphic Matroids
Nathan Bowler, Daryl Funk, Daniel Slilaty
This is a revised version of our original paper (arXiv:1808.00489v2) incorporating the corrections published in a corrigendum (arXiv:1808.00489v3). Our main theorem as originally s…