The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
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
An algebraic theory of graph reduction
Journal of the ACM (JACM)
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Structural properties of context-free sets of graphs generated by vertex replacement
Information and Computation
The monadic second-order logic of graphs X: linear orderings
Theoretical Computer Science
Basic notions of universal algebra for language theory and graph grammars
Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: volume I. foundations
The expression of graph properties and graph transformations in monadic second-order logic
Handbook of graph grammars and computing by graph transformation
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Series-parallel languages and the bounded-width property
Theoretical Computer Science
Rationality in algebras with a series operation
Information and Computation
The Book of Traces
The Complexity of First-Order and Monadic Second-Order Logic Revisited
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Recognizability Equals Monadic Second-Order Definability for Sets of Graphs of Bounded Tree-Width
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
The monadic second-order logic of graphs XIV: uniformly sparse graphs and edge set quantifications
Theoretical Computer Science
Towards a language theory for infinite N-free pomsets
Theoretical Computer Science
Regular sets of infinite message sequence charts
Information and Computation
Extremal Graph Theory
Journal of Automata, Languages and Combinatorics
On the logical definability of centrain graph and poset languages
Journal of Automata, Languages and Combinatorics
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Recognizable sets of graphs, hypergraphs and relational structures: a survey
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Parameterized Complexity
Algebraic recognizability of regular tree languages
Theoretical Computer Science - The art of theory
Recognizability, hypergraph operations, and logical types
Information and Computation
Vertex-minors, monadic second-order logic, and a conjecture by Seese
Journal of Combinatorial Theory Series B
On the Recognizability of Arrow and Graph Languages
ICGT '08 Proceedings of the 4th international conference on Graph Transformations
Graph operations characterizing rank-width
Discrete Applied Mathematics
Recognizability, hypergraph operations, and logical types
Information and Computation
Graph operations characterizing rank-width and balanced graph expressions
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Automata on directed graphs: edge versus vertex marking
ICGT'06 Proceedings of the Third international conference on Graph Transformations
Hi-index | 5.23 |
Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite congruences. Applications to the construction of efficient algorithms and to the theory of context-free sets of graphs follow naturally. The class of recognizable sets depends on the signature of graph operations. We consider three signatures related respectively to Hyperedge Replacement (HR) context-free graph grammars, to Vertex Replacement (VR) context-free graph grammars, and to modular decompositions of graphs. We compare the corresponding classes of recognizable sets. We show that they are robust in the sense that many variants of each signature (where in particular operations are defined by quantifier-free formulas, a quite flexible framework) yield the same notions of recognizability. We prove that for graphs without large complete bipartite subgraphs, HR-recognizability and VR-recognizability coincide. The same combinatorial condition equates HR-context-free and VR-context-free sets of graphs. Inasmuch as possible, results are formulated in the more general framework of relational structures.