Publications (16)
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…
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.
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 …
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…
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…
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…