The most congested cutset: deriving a tight lower bound for the chromatic number in the RWA problem

Routing and wavelength assignment (RWA) is an important issue in the design of routing protocols in an all-optical network. A solution for the RWA problem should determine the least possible number of wavelengths, also known as the chromatic number. In this letter, we introduce the concept of cutset congestion, and show that the congestion of the most congested cutset of a graph representing the network is a tight lower bound for the chromatic number in the RWA problem. In contrast to other existing techniques, our method can be applied to any network and any traffic pattern.