All right, what are you trying to find out about signed graphs and their associated matroid(s)?

Ok, here's the scoop. It turns out that the bias matroid of a signed graph is representable over all fields whose characteristic is not two (Zaslavsky, Signed Graphs); in particular, it is always GF(3)-representable. Now, Whittle's results (at least those I'm interested in!) deal with the classes of all matroids representable over GF(3) and another field. Combining the results of these two papers, it's seen that these bias matroids of signed graphs can come in three "flavors":

• Regular, which are representable over every field.
• Near-regular, which are representable over every field except possibly GF(2).
• Dyadic, which are representable over every field of characteristic other than 2.

(Among other things, this means that the bias matroid of any signed graph is dyadic.) My research has been centered on this work so far.

[Updated 15 July 1999] Since I first wrote this page, I completed a characterization of the above problem. I am now working on questions about the separability of the bias matroid, determining uniqueness of representation (as a signed graph) of the bias matroid of a signed graph, and determining when a given matroid has a signed-graph realization.

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