Easy problems for tree-decomposable graphs
Journal of Algorithms
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
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
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Branch-width, parse trees, and monadic second-order logic for matroids
Journal of Combinatorial Theory Series B
MSOL partitioning problems on graphs of bounded treewidth and clique-width
Theoretical Computer Science
Computing the Tutte Polynomial on Graphs of Bounded Clique-Width
SIAM Journal on Discrete Mathematics
Rank-width is less than or equal to branch-width
Journal of Graph Theory
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
On the Algorithmic Effectiveness of Digraph Decompositions and Complexity Measures
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Graph operations characterizing rank-width
Discrete Applied Mathematics
Communication: On complexity of Minimum Leaf Out-Branching problem
Discrete Applied Mathematics
Minimum leaf out-branching and related problems
Theoretical Computer Science
On Digraph Width Measures in Parameterized Algorithmics
Parameterized and Exact Computation
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
Computing graph polynomials on graphs of bounded clique-width
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
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In this paper we develop new algorithmic machinery for solving hard problems on graphs of bounded rank-width and on digraphs of bounded bi-rank-width in polynomial (XP, to be precise) time. These include, particularly, graph coloring and chromatic polynomial problems, the Hamiltonian path and c-min-leaf outbranching, the directed cut, and more generally MSOL-partitioning problems on digraphs. Our focus on a formally clean and unified approach for the considered algorithmic problems is in contrast with many previous published XP algorithms running on graphs of bounded clique-width, which mostly used ad hoc techniques and ideas. The new contributions include faster algorithms for computing the chromatic number and the chromatic polynomial on graphs of bounded rank-width, and new algorithms for solving the defective coloring, the min-leaf outbranching, and the directed cut problems.