12 citations · 78 across the 26 of their papers we have counts for
30 papers
Clonal cores and flexipaths in matroids
Nick Brettell, James Oxley, Charles Semple +1
A partitioned matroid consists of a matroid and a partition of its ground set. As such structures arise frequently in struc…
What is a 4-connected matroid?
Nick Brettell, Susan Jowett, James Oxley +2
The {\em breadth} of a tangle in a matroid is the size of the largest spanning uniform submatroid of the tangle matroid of . A matroid is {\em weakly…
The excluded minors for 2- and 3-regular matroids
Nick Brettell, James Oxley, Charles Semple +1
The class of 2-regular matroids is a natural generalisation of regular and near-regular matroids. We prove an excluded-minor characterisation for the class of 2-regular matroids. T…
Excluded minors are almost fragile II: essential elements
Nick Brettell, James Oxley, Charles Semple +1
Let be an excluded minor for the class of -representable matroids for some partial field , let be a -connected strong -stabilizer tha…
Fractal classes of matroids
Dillon Mayhew, Mike Newman, Geoff Whittle
A minor-closed class of matroids is (strongly) fractal if the number of n-element matroids in the class is dominated by the number of n-element excluded minors. We conjecture that…
On Density-Critical Matroids
Rutger Campbell, Kevin Grace, James Oxley +1
For a matroid having rank-one flats, the density is unless , in which case . A matroid is density-critical if all of its proper min…