This paper presents a new algorithm for effectively assigning wavelengths to ligthpaths in a multihop wavelength division multiplexed (WDM) optical network, wherein the physical medium consists of optical fiber segments interconnected by wavelength selective optical switches. WDM permits a limited number of wavelengths to be re-used among various fiber links, thereby offering a very high aggregate capacity. For a given network, we first construct its auxiliary graph and then formulate wavelength assignment as a graph coloring problem on the auxiliary graph. However, we do not follow the conventional two-step procedure, unlike most of the existing techniques. While generating the auxiliary graph from the given physical topology and the given set of ligthpath requests, simultaneously we apply a dynamic coloring technique to assign colors (i.e., wavelengths) to nodes (i.e., lightpaths) on the fly. The number of colors needed at the end of the algorithm represents the number of wavelengths required for the network. The algorithm is proven to be correct, and its complexity is analyzed. The performance of the algorithm is tested on several networks for various lightpath demands through extensive simulations. The coloring scheme, blocking performance and timing efficiencies are studied and compared with the existing best-known wavelength assignment heuristics. It is found that, for a wide range of network sizes and lightpath requests, the proposed algorithm performs equally well, when compared with the existing ones.