The Vertex Coloring Problem and its generalizations

This is a summary of the author’s PhD thesis supervised by Paolo Toth and defended on 29 May 2007 at the Università di Bologna. The thesis is written in English and is available from the author upon request. The first part of this work deals with the Vertex Coloring Problem and its generalizations, for which models, bounds and algorithms are proposed. The Second Part is dedicated to a different problem on graphs, namely a Routing Problem in telecommunication networks where not only the efficiency, but also the fairness of the solution is considered.