937 citations
- MacDiarmid Institute for Advanced Materials and NanotechnologyNZ72 papers
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16 papers · 1 filter
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…
Computing excluded minors for classes of matroids representable over partial fields
Nick Brettell, Rudi Pendavingh
We describe an implementation of a computer search for the "small" excluded minors for a class of matroids representable over a partial field. Using these techniques, we enumerate…
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…
On Ramsey-minimal infinite graphs
Jordan Mitchell Barrett, Valentino Vito
For fixed finite graphs , , a common problem in Ramsey theory is to study graphs such that , i.e. every red-blue coloring of the edges of produces either…
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…