The assignment of wavelengths to lightpaths in WDM networks is a crucial problem that needs to be solved efficiently. However, the coloring of the graph representing the lightpaths and their interference is an NP-hard problem. The parameterized Complexity Theory offers an attractive theoretical framework for the derivation of exact solutions with lower complexity than those derived using the Classical Complexity Theory since it transfers the exponentiality dependence from the input parameters describing the network to a parameter called modulator which can be bounded. This paper presents an algorithm for wavelength assignment in transparent WDM networks. Numerical examples illustrate the benefits of the employment of this new theory for the solution of the wavelength assignment problem.