Easy problems for tree-decomposable graphs
Journal of Algorithms
Handbook of theoretical computer science (vol. B)
The monadic second-order logic of graphs VII: graphs as relational structures
Theoretical Computer Science - Special issue on logic and applications to computer science
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Monadic second-order definable graph transductions: a survey
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Structural properties of context-free sets of graphs generated by vertex replacement
Information and Computation
Logical description of context-free graph languages
Journal of Computer and System Sciences
Node replacement graph grammars
Handbook of graph grammars and computing by graph transformation
Hyperedge replacement graph grammars
Handbook of graph grammars and computing by graph transformation
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Graph Grammars and Tree Transducers
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
The parametrized complexity of knot polynomials
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Recognizability, hypergraph operations, and logical types
Information and Computation
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Recognizability, hypergraph operations, and logical types
Information and Computation
On equivalent representations of infinite structures
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Linear recurrence relations for graph polynomials
Pillars of computer science
F-rank-width of (edge-colored) graphs
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
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Relational structures offer a common framework for handling graphs and hypergraphs of various kinds. Operations like disjoint union, the creation of new relations by means of quantifier-free formulas, and relabellings of relations make it possible to denote them using algebraic expressions. It is known that every monadic second-order property of a structure is verifiable in time proportional to the size of such an algebraic expression defining it. We prove here that this result remains true if we also use in these algebraic expressions a fusion operation that fuses all elements of the domain satisfying some unary predicate. The value mapping from these algebraic expressions to the structures they denote is a monadic second-order definable transduction, which means that the structure is definable inside the tree representing the algebraic expression by monadic second-order formulas. It follows (by using results of other articles) that, with this fusion operation, we cannot generate more graph families, but we can generate them with less unary auxiliary predicates. We also obtain clear-cut characterizations of Vertex Replacement and Hyperedge Replacement context-free graph grammars in terms of four types of operations, amongst which is the fusion of vertices satisfying a specified predicate.