GRAPH DECOMPOSITIONS AND MONADIC SECOND ORDER LOGIC

A tree decomposition is a tool which allows for analysis of the underlying tree structure of graphs which are not trees. Given a class of graphs with bounded tree width, many NP-complete problems can be computed in linear time for graphs in the class. Clique width of a graph G is a measure of the number of labels required to con-struct G using several particular graph operations. For any integer k, both the class of graphs with tree width at most k and the class of graphs with clique width at most k have a decidable monadic second order theory. In this paper we explore some recent results in applying these graph measures and their relation to monadic second order logic