Multicoloring and Wavelength Assignment in WDM all-optical Networks

This paper deals with the wavelength assignment problem in WDM all-optical networks. This problem can be abstracted as a multicoloring on a weighted conflict graph. The main focus of this work is to obtain the relationship between the wavelength assignment and the multicoloring problems. We, first, establish a new result regarding multicoloring problem in which we provide a tight bound for any graph. Afterwards, considering off-line wavelength assignment problem in all-optical networks particularly for certain routing patterns, we show that coloring all paths of this routing is the same as the multicoloring problem of the associated conflict graph.