
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
.





