5 papers · 1 filter
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…
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…
Defining bicircular matroids in monadic logic
Daryl Funk, Dillon Mayhew, Mike Newman
We conjecture that the class of frame matroids can be characterised by a sentence in the monadic second-order logic of matroids, and we prove that there is such a characterisation…
Effective versions of two theorems of Rado
Jason Bell, Daryl Funk, Byoung Du Kim +1
Let be a representable matroid on elements. We give bounds, in terms of , on the least positive characteristic and smallest field over which is representable.
On excluded minors for classes of graphical matroids
Daryl Funk, Dillon Mayhew
Frame matroids and lifted-graphic matroids are two distinct minor-closed classes of matroids, each of which generalises the class of graphic matroids. The class of quasi-graphic ma…