Problem of the Week
Hilton Memorial Lecture
Signed-graphic matroids are a genuine generalization of graphic matroids. A lot of research has been done on determining to what extent we can transfer properties of graphic matroids to signed-graphic matroids.
In this talk I focus on a theorem of Matthews from the 1970s that characterizes graphs whose bicircular matroids are graphic. We characterize graphs whose bicircular matroids are signed-graphic. A consequence of the characterization is that there are not very many 3-connected matroids that are both signed-graphic and bicircular.
I will also discuss the intersection of the class of signed-graphic matroids with other well-known classes of matroids.