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math.CO2021
Small cocircuits in minimally vertically -connected matroids
James Oxley, Zach Walsh
Halin proved that every minimally -connected graph has a vertex of degree . More generally, does every minimally vertically -connected matroid have a -element cocircuit…
math.CO2021
A new matroid lift construction and an application to group-labeled graphs
Zach Walsh
A well-known result of Brylawski constructs an elementary lift of a matroid from a linear class of circuits of . We generalize this result by showing how to construct a rank…
math.CO2021
Excluding a line from -representable matroids
Jim Geelen, Peter Nelson, Zach Walsh
For each positive integer and each sufficiently large integer , we show that the maximum number of elements of a simple, rank-, -representable matroid with no…