Bouchet's Conjecture states that every signed graph (equivalent to a bidirected graph) admits a nowhere zero 6-flow.
I will introduce signed and bidirected graphs, circular and integral flows on signed graphs, and the matroid of a signed graph. The main result of this talk will be proving an upper bound on the circular flow number of a signed graph based on the edge connectivity of the underlying graph, which is a partial result towards Bouchet's Conjecture. The proof of this theorem will make use of some elementary facts about the matroid of a signed graph.
The results in this talk are from a paper by Raspaud & Zhu by the same title.