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The notion of a recognizable set of finite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic… Expand
Abstract 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… Expand
Handbook of Theoretical Computer Science, Volume…
Publisher Summary This chapter presents three mathematical tools that can be used to describe graph-grammars and the sets generated by them. The chapter describes graph properties by logical formulas… Expand
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the… Expand
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 of… Expand
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 propei… Expand
Graphs are finite and handled as relational structures. We give some answers to the following general questions:
1.
(1) For which classes of graphs C is it possible to specify a linear ordering of… Expand
Abstract. Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On… Expand
Abstract In every undirected graph or, more generally, in every undirected hypergraph of bounded rank, one can specify an orientation of the edges or hyperedges by monadic second-order formulas using… Expand