The fractional edge chromatic number of a graph G is the fractional analog of the edge chromatic number, denoted χ_f^, (G) by Scheinerman and Ullman. It can be defined as χ_f^, (G) = χ_f(L(G)), where χ_f(G) is the fractional chromatic number of G and L(G) is the line graph of G. There exists a polynomial-time algorithm for computing the fractional edge chromatic number (Scheinerman and Ullman 2011, pp. 86-87).

edge chromatic number | fractional chromatic number