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math.CO2020
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…
math.CO2020
Obstructions for bounded branch-depth in matroids
J. Pascal Gollin, Kevin Hendrey, Dillon Mayhew +1
DeVos, Kwon, and Oum introduced the concept of branch-depth of matroids as a natural analogue of tree-depth of graphs. They conjectured that a matroid of sufficiently large branch-…