Vertex coloring edge-weighted digraphs

We consider vertex colorings of edge-weighted graphs.We give tight upper and lower bounds on the chromatic number in terms of degree parameters.The results have implications for wireless scheduling in physical models of interference. A coloring of a digraph with non-negative edge weights is a partition of the vertex set into independent sets, where a set is independent if the weighted in-degree of each node within the set is less than 1. We give constructive optimal bounds on the chromatic number in terms of maximum in-degree and inductiveness of the graph.