The chromatic covering number of a graph

Following [1], we investigate the problem of covering a graph G with induced subgraphs G(1),..., G(k) of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciprocals of the chromatic numbers of the G,'s containing u is at least 1. The existence of such "chromatic coverings" provides some bounds on the chromatic number of G. (c) 2005 Wiley Periodicals, Inc.