Fractional Q-coloring of graphs

Abstract

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

Edge-colouring of graphs and hereditary graph properties

“…One of the first papers dealing with this topic is the work of Ha luszczak and Vateha [8]. Czap and Mihók [3] considered edge-colourings in which the edges coloured by the same colour induce a subgraph of some hereditary property P. Another research problem on non-proper edge-colourings and hereditary properties is described and studied in [4].…”