1 citations · 1 across the 5 of their papers we have counts for
7 papers
Weighted coloop splittings in rank six
James Dylan Douthitt, Lee Kennard, Josef Komissar
With a view toward applications in Riemannian geometry, we explore coloop splitting properties of regular matroids. Nienhaus showed by classification in rank four that a regular ma…
Degeneracy: From Graphs to Matroids
Allan Bickle, James Dylan Douthitt, Wayne Ge +1
A graph is -degenerate if every subgraph has a vertex of degree at most . We extend this notion to matroids, defining a loopless matroid to be -degenerate if every res…
Higher cosystoles of matroids
James Dylan Douthitt, Elana Israel, Lee Kennard
We define a matroid invariant called the three-cosystole that is related to higher notions of cogirth for weighted matroids, and we prove an optimal upper bound for it in the class…
Rainbow triangles and the Erdős-Hajnal problem in projective geometries
Carolyn Chun, James Dylan Douthitt, Wayne Ge +3
We formulate a geometric version of the Erdős-Hajnal conjecture that applies to finite projective geometries rather than graphs, in both its usual 'induced' form and the multicolou…
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…
Chordal matroids arising from generalized parallel connections
James Dylan Douthitt, James Oxley
A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeate…