The monadic second-order logic of graphs III : tree-decompositions, minors and complexity issues

Abstract

We relate the tree-decompositions of hypergraphs introduced by Robertson and Seymour to the finite and infinite algebraic expressions introduced by Bauderon and Courcelle. We express minor inclusion in monadic second-order logic, and we obtain grammatical characterizations of certain sets of graphs defined by excluded minors. We show how tree-decompositions can be used to construct quadratic algorithms deciding monadic second-order properties on hypergraphs ofbounded tree-width.