SFU Discrete Math Seminar: Zhouningxin Wang

In this talk, we consider analogs of Jaeger's circular flow conjecture and its dual Jaeger-Zhang conjecture in signed graphs. We will first give the notions of circular coloring and circular flow in signed graphs, and then show that every (6k-2)-edge-connected Eulerian signed graph admits a circular 4k/(2k-1)-flow and that every signed bipartite planar graph of negative-girth at least 6k-2 admits a circular 4k/(2k-1)-coloring (equivalently, admits a homomorphism to a negative cycle of length 2k). We also provide some recent results about circular flow indices of signed graphs with high edge-connectivities.
This is based on joint work with Jiaao Li, Reza Naserasr, and Xuding Zhu.