# nowhere-zero flow, edge-colorings, regular graphs

## Circular flow number of regular class 1 graphs ★★

Author(s): Steffen

A nowhere-zero -flow on is an orientation of together with a function from the edge set of into the real numbers such that , for all , and . The circular flow number of is inf has a nowhere-zero -flow , and it is denoted by .

A graph with maximum vertex degree is a class 1 graph if its edge chromatic number is .

**Conjecture**Let be an integer and a -regular graph. If is a class 1 graph, then .