Fractional Q-Edge-Coloring of Graphs

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let be an additive hereditary property of graphs. A -edge-coloring of a simple graph is an edge coloring in which the edges colored with the same color induce a subgraph of property . In this paper we present some results on fractional -edge-colorings. We determine the fractional -edge chromatic number for matroidal properties of graphs