This paper begins an investigation of the monadic second-order logic of graphs and of sets of graphs, using techniques from universal algebra, and the theory of formal languages. (By a graph, we meanâ€¦ (More)

Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs ofâ€¦ (More)

Graphs are finite and handled as relational structures. We give some answers to the following general questions: (1) For which classes of graphs % is it possible to specify a linear ordering of theâ€¦ (More)

Hierarchical decompositions of graphs are interesting for algorithmic purposes. Many NP complete problems have linear complexity on graphs with tree-decompositions of bounded width. We investigateâ€¦ (More)

Abstrwt. Infinite trees naturally arise in the formaliration and the c~udy of fhc \cm;lntic*, 01 prog-amming languages. This paper investigates some of their i:omninatorial and :iIgcbri\ic propeiâ€¦ (More)

We define an algebraic structure for the set of finite graphs, a notion of graph expression for defining them, and a complete set of equational rules for manipulating graph expressions. (By agraph weâ€¦ (More)

A countable graph can be considered as the value of a certain infinite expression, represented itself by an infinite tree. We establish that the set of finite or infinite (expression) treesâ€¦ (More)

We discuss the parametrized complexity of counting and evaluation problems on graphs where the range of counting is de nable in monadic second-order logic (MSOL). We show that for bounded tree-widthâ€¦ (More)