


Abstract: In his attempt to attack the (then) 4colorconjecture, Tutte in 1950s discovered the nowhere zero flows, and founded the theory on nowhere zero flows of graphs. He proved that a plane map is 4facecolorable if and only if the corresponding graph $G$ has a nowhere zero 4flow. Tutte's fascinating conjectures on nowhere zero flows have drawn the attention of many researchers over the decades, and remain open as of today. Group connectivity of graphs is the nonhomogeneous version of the nowhere zero flows, and was first studied by Jaeger, Linial, Payan and Tarsi in 1992 ([J. Combinatorial Theory, Ser. B 56 (1992) 165182]). In this talk, we shall survey the latest results and developments on the topic.
