J. Douthitt

activity

20242026

collaborators

5 papers

math.CO2026

Degeneracy: From Graphs to Matroids

Allan Bickle, James Dylan Douthitt, Wayne Ge +1

A graph is $k$ -degenerate if every subgraph has a vertex of degree at most $k$ . We extend this notion to matroids, defining a loopless matroid $M$ to be $k$ -degenerate if every res…

math.CO2026

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…

math.CO2025

Rainbow triangles and the ErdÅs-Hajnal problem in projective geometries

Carolyn Chun, James Dylan Douthitt, Wayne Ge +3

We formulate a geometric version of the ErdÅs-Hajnal conjecture that applies to finite projective geometries rather than graphs, in both its usual 'induced' form and the multicolo…

math.CO2024

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 $M (C_{4})$ as an induced minor and the class of matroids with no member of ${M (C_{4}), M (K_{4})}$ as an induced minor. In…