Graphic presentations of isotropic systems
Journal of Combinatorial Theory Series A
Connectivity of isotropic systems
Proceedings of the third international conference on Combinatorial mathematics
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
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
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Edge dominating set and colorings on graphs with fixed clique-width
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
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithms for vertex-partitioning problems on graphs with fixed clique-width
Theoretical Computer Science
Graphs of bounded rank-width
A Parametrized Algorithm for Matroid Branch-Width
SIAM Journal on Computing
Journal of Combinatorial Theory Series B
Clique-width minimization is NP-hard
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Vertex-minors, monadic second-order logic, and a conjecture by Seese
Journal of Combinatorial Theory Series B
The branchwidth of graphs and their cycle matroids
Journal of Combinatorial Theory Series B
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
Clique-width: on the price of generality
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Intractability of Clique-Width Parameterizations
SIAM Journal on Computing
Exploiting restricted linear structure to cope with the hardness of clique-width
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Polynomial-time recognition of clique-width ≤3 graphs
Discrete Applied Mathematics
Recognition of probe distance-hereditary graphs
Discrete Applied Mathematics
On the minimum degree up to local complementation: bounds and complexity
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
A SAT approach to clique-width
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width
Fundamenta Informaticae - MFCS & CSL 2010 Satellite Workshops: Selected Papers
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Rank-width was defined by Oum and Seymour [2006] to investigate clique-width. They constructed an algorithm that either outputs a rank-decomposition of width at most f(k) for some function f or confirms that rank-width is larger than k in time O(|V|9log |V|) for an input graph G = (V,E) and a fixed k. We develop three separate algorithms of this kind with faster running time. We construct an O(|V|4)-time algorithm with f(k) = 3k + 1 by constructing a subroutine for the previous algorithm; we avoid generic algorithms minimizing submodular functions used by Oum and Seymour. Another one is an O(|V|3)-time algorithm with f(k) = 24k, achieved by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hliněný [2005]. Finally we construct an O(|V|3)-time algorithm with f(k) = 3k − 1 by combining the ideas of the two previously cited papers.