4 papers
Unavoidable Minors of Matroids with Minimum Cocircuit Size Four
Matthew Mizell, James Oxley
In 1963, Halin and Jung proved that every simple graph with minimum degree at least four has or as a minor. Mills and Turner proved an analog of this theorem by s…
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…
Classes of binary matroids with small lists of excluded induced minors
James Dylan Douthitt, James Oxley
In earlier work, we characterized the class of matroids with no as an induced minor and the class of matroids with no member of as an induced minor. In…
Chordal matroids arising from generalized parallel connections II
James Dylan Douthitt, James Oxley
In 1961, Dirac showed that chordal graphs are exactly the graphs that can be constructed from complete graphs by a sequence of clique-sums. In an earlier paper, by analogy with Dir…