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 overview presents the main definitions, results and open problems and tries to answer some frequently asked questions.