7 citations · 16 across the 12 of their papers we have counts for
16 papers
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…
There are only a finite number of excluded minors for the class of bicircular matroids
Matt DeVos, Daryl Funk, Luis Goddyn +1
We show that the class of bicircular matroids has only a finite number of excluded minors. Key tools used in our proof include representations of matroids by biased graphs and the…
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…
Tree automata and pigeonhole classes of matroids: II
Daryl Funk, Dillon Mayhew, Mike Newman
Let be a sentence in the counting monadic second-order logic of matroids and let be a finite field. Hliněný's Theorem says that we can test whether -re…
Tree automata and pigeonhole classes of matroids: I
Daryl Funk, Dillon Mayhew, Mike Newman
Hlineny's Theorem shows that any sentence in the monadic second-order logic of matroids can be tested in polynomial time, when the input is limited to a class of F-representable ma…
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…
Short rainbow cycles in graphs and matroids
Matt DeVos, Matthew Drescher, Daryl Funk +5
Let be a simple -vertex graph and be a colouring of with colours, where each colour class has size at least . We prove that contains a rainbow cycl…
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…
How many delta-matroids are there?
Daryl Funk, Dillon Mayhew, Steven D. Noble
We give upper and lower bounds on the number of delta-matroids, and on the number of even delta-matroids.
Matrix representations of frame and lifted-graphic matroids correspond to gain functions
Daryl Funk, Irene Pivotto, Daniel Slilaty
Let be a 3-connected matroid and let be a field. Let be a matrix over representing and let be a biased graph representing .…
Almost balanced biased graph representations of frame matroids
Matt DeVos, Daryl Funk
Given a 3-connected biased graph with a balancing vertex, and with frame matroid nongraphic and 3-connected, we determine all biased graphs with . As…
On excluded minors of connectivity 2 for the class of frame matroids
Matt DeVos, Daryl Funk, Irene Pivotto
We investigate the set of excluded minors of connectivity 2 for the class of frame matroids. We exhibit a list of 18 such matroids, and show that if is such an ex…
Graphical representations of graphic frame matroids
Rong Chen, Matt DeVos, Daryl Funk +1
A frame matroid M is graphic if there is a graph G with cycle matroid isomorphic to M. In general, if there is one such graph, there will be many. Zaslavsky has shown that frame ma…
When does a biased graph come from a group labelling?
Matt DeVos, Daryl Funk, Irene Pivotto
A biased graph consists of a graph together with a collection of distinguished cycles of , called balanced cycles, with the property that no theta subgraph contains exactly…