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The smallest class of binary matroids closed under direct sums and complements
James Oxley, Jagdeep Singh
The class of cographs or complement-reducible graphs is the class of graphs that can be generated from using the operations of disjoint union and complementation. By analogy,…
Small cocircuits in minimally vertically -connected matroids
James Oxley, Zach Walsh
Halin proved that every minimally -connected graph has a vertex of degree . More generally, does every minimally vertically -connected matroid have a -element cocircuit…
On the Cogirth of Binary Matroids
Cameron Crenshaw, James Oxley
The cogirth, , of a matroid is the size of a smallest cocircuit of . Finding the cogirth of a graphic matroid can be done in polynomial time, but Vardy showed in…
Generalizing Cographs to 2-Cographs
James Oxley, Jagdeep Singh
A graph in which every connected induced subgraph has a disconnected complement is called a cograph. Such graphs are precisely the graphs that do not have the 4-vertex path as an i…