Graph structure is a flexible concept covering many different types of graph properties. Hierarchical decompositions yielding the notions of tree-width and clique-width, expressed by terms written with appropriate graph operations and associated with Monadic Second-order Logic are important tools for the construction of Fixed-Parameter Tractable algorithms and also for the extension of methods and results of Formal Language Theory to the description of sets of finite graphs. This informal

more »

... ew presents the main definitions, results and open problems and tries to answer some frequently asked questions. Supported by the GRAAL project of "Agence Nationale pour la Recherche".