 
Summary: On the Fractional Chromatic Index of a Graph
and its Complement
David Avis,1
Caterina De Simone2
and Bruce Reed1
School of Computer Science, McGill University,
3480 University Street, Montreal, Canada, H3A2A7.1
Istituto di Analisi dei Sistemi ed Informatica (IASI),
CNR, Viale Manzoni 30, 00185 Rome, Italy.2
24 September 2004
ABSTRACT
The chromatic index e(G) of an undirected graph G is the minimum
number of matchings needed to partition its edge set. Let (G) denote the maxi
mum vertex degree of G, and let G denote the complement of G. Jensen and
Toft conjectured that for a graph G with an even number of vertices, either
e(G) = (G) or e(G) = (G). We prove a fractional version of this conjec
ture.
1. The Introduction
The chromatic index e(G) of a graph G = (V(G), E(G)) is the minimum number of
matchings needed to partition its edge set (for the definition of matching and other standard
