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Full-Text Articles in Physical Sciences and Mathematics
The Family Of Bicircular Matroids Closed Under Duality, Vaidy Sivaraman, Daniel Slilaty
The Family Of Bicircular Matroids Closed Under Duality, Vaidy Sivaraman, Daniel Slilaty
Mathematics and Statistics Faculty Publications
We characterize the 3-connected members of the intersection of the class of bicircular and cobi- circular matroids. Aside from some exceptional matroids with rank and corank at most 5, this class consists of just the free swirls and their minors.
Describing Quasi-Graphic Matroids, Nathan Bowler, Daryl Funk, Dan Slilaty
Describing Quasi-Graphic Matroids, Nathan Bowler, Daryl Funk, Dan Slilaty
Mathematics and Statistics Faculty Publications
The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and liftedgraphic matroids introduced earlier by Zaslavsky. For each biased graph (G, B) Zaslavsky defined a unique lift matroid L(G, B) and a unique frame matroid F(G, B), each on ground set E(G). We show that in general there may be many quasi-graphic matroids on E(G) and describe them all: for each graph G and partition (B, L, F) of its cycles such that B satisfies the theta property and each cycle in L meets each cycle in F, there …