9 papers · 1 filter
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 Kővari-Sós-Turán theorem for -representable matroids
Wayne Ge
In this paper, we establish an analogue of the Kővari-Sós-Turán Theorem for -representable matroids. For , we show that if is a rank- si…
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…
Reconstruction of C_4-free graphs from the set of closed neighborhoods and digital convexity
Steffen Borgwardt, MacKenzie Carr, Ce Chen +4
Fomin, Kratochvíl, Lokshtanov, Mancini, and Telle showed that every -free graph is reconstructible from the \emph{multiset} of closed neighborhoods. We strengthen their resu…