Edge Colorings and Circular Flow Numbers of Regular Graphs

The article characterizes 2t+1-regular graphs with circular flow number 2+22t-1. For t=1 this is Tutte's characterization of cubic graphs with flow number 4. The class of cubic graphs is the only class of odd regular graphs where a flow number separates the class 1 graphs from the class 2 graphs. We finally state some conjectures and relate them to Jaeger's circular flow conjecture and Tutte's 3-flow conjecture.