Abstract

The weighted coloured-edge graph is a graph for which each edge is assigned both a positive weight and a discrete colour, and can be used to model transportation and computer networks in which there are multiple transportation modes. In such a graph paths are compared by their total weight in each colour, resulting in a Pareto set of minimal paths form one vertx to another. This paper will give a tight upper bound on th ecardinality of a minimal set of paths for any weighted coloured-edge graph.