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Atlantic Graph Theory Seminar
September 20, 2023 @ 3:30 pm - 4:30 pm
Title: On flows (and group-connectivity) in signed graphs
In this talk we’ll start by discussing flows in signed graphs and how it generalizes the usual notion of integer flows in graphs. In particular, flow-colouring duality of graphs in the plane can be re-interpreted using signed graphs in the projective plane. Also, where a flow in a graph can be viewed as a sum of flows on cycles, in a signed graph, positive cycles and barbells are the key structures to consider. We’ll share a new result, joint with K. Nurse and A. Brewer-Castano, about flows in 3-edge-connected signed graphs. In fact, this result holds for the stronger notion of group-connectivity, which was introduced as a generalization of flows by Jaeger, Linial, Payan, and Tarsi in 1992. Building on their work and also on work by Li, Luo, Ma and Zhang (2018), we (mostly) establish a group-connected analog of Seymour’s 6-flow Theorem for signed graphs.