The fractional edge chromatic number of a graph is the fractional analog of the edge
chromatic number, denoted by Scheinerman and Ullman (2011). It can be defined
as

There exists a polynomial-time algorithm for computing the fractional edge chromatic number (Scheinerman and Ullman 2011, pp. 86-87).

If the edge chromatic number of a graph equals its maximum vertex degree (i.e., if a graph is class
1), then the fractional edge chromatic number also equals . This follows from the general principle for fractional
objects that

(2)

and the fact that

(3)

(Scheinerman and Ullman 2011, p. 80), so combining gives

The flower snark is an example of a graph for which the edge
chromatic number and fractional edge chromatic number are both integers, but (Scheinerman and Ullman 2001, p. 96).