Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series 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
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
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
Mona: Monadic Second-Order Logic in Practice
TACAS '95 Proceedings of the First International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Query efficient implementation of graphs of bounded clique-width
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Journal of Combinatorial Theory Series B
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Clique-width minimization is NP-hard
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Recognizability, hypergraph operations, and logical types
Information and Computation
The recognizability of sets of graphs is a robust property
Theoretical Computer Science
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
The relative clique-width of a graph
Journal of Combinatorial Theory Series B
Vertex-minor reductions can simulate edge contractions
Discrete Applied Mathematics
Rank-width is less than or equal to branch-width
Journal of Graph Theory
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Graph operations characterizing rank-width and balanced graph expressions
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Finding branch-decompositions and rank-decompositions
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Parameterized Complexity
On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width
Discrete Applied Mathematics
H-join decomposable graphs and algorithms with runtime single exponential in rankwidth
Discrete Applied Mathematics
F-rank-width of (edge-colored) graphs
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Well-quasi-ordering of matrices under Schur complement and applications to directed graphs
European Journal of Combinatorics
A unified approach to polynomial algorithms on graphs of bounded (bi-)rank-width
European Journal of Combinatorics
Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width
Fundamenta Informaticae - MFCS & CSL 2010 Satellite Workshops: Selected Papers
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Graph complexity measures such as tree-width, clique-width and rank-width are important because they yield Fixed Parameter Tractable algorithms. These algorithms are based on hierarchical decompositions of the considered graphs, and on boundedness conditions on the graph operations that, more or less explicitly, recombine the components of decompositions into larger graphs. Rank-width is defined in a combinatorial way, based on a tree, and not in terms of graph operations. We define operations on graphs that characterize rank-width and help for the construction of Fixed Parameter Tractable algorithms, especially for problems specified in monadic second-order logic.