From the 1 of 9 linked papers with an AI index.
9 papers
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…
The KÅvari-Sós-Turán theorem for -representable matroids
Wayne Ge
The paper proves a Kővari–Sós–Turán type extremal bound for simple matroids representable over a finite field GF(q), showing that avoiding a complete bipartite graph restriction li…
Unavoidable flats in connected regular matroids
Wayne Ge
This paper proves that every -connected regular matroid of sufficiently large rank has a -connected graphic flat of large rank. Furthermore, we explicitly determine a list of…
The connected binary matroids with a pair of elements in no non-spanning circuits
Wayne Ge, James Oxley, Jagdeep Singh
Let be a simple connected binary matroid, and let and be distinct elements of . It is well known that, when the only circuits containing are spanning, is a c…
Super-minimally -connected matroids
Wayne Ge, James Oxley
A super-minimally -connected matroid is a -connected matroid having no proper -connected restriction of size at least . This extends the corresponding concept for gr…
Unavoidable cycle-contraction minors of large -connected graphs
Wayne Ge, James Oxley
It is well known that every sufficiently large connected graph has, as an induced subgraph, , , or an -vertex path. A 2023 paper of Allred, Ding, and Oporowski ide…