Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees
Journal of Algorithms
Clique partitions, graph compression and speeding-up algorithms
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Nearest common ancestors: a survey and a new distributed algorithm
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
The edge-disjoint path problem is NP-complete for series-parallel graphs
Discrete Applied Mathematics - Special issue on selected papers from First Japanese-Hungarian Symposium for Discrete Mathematics and its Applications
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
On the Relationship between Clique-Width and Treewidth
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
New Graph Classes of Bounded Clique-Width
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Minimizing nLC-width is nP-complete
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Polynomial algorithms for protein similarity search for restricted mRNA structures
Information Processing Letters
Solving problems on recursively constructed graphs
ACM Computing Surveys (CSUR)
The NLC-width and clique-width for powers of graphs of bounded tree-width
Discrete Applied Mathematics
Spanning cactus of a graph: Existence, extension, optimization, and approximation
Discrete Applied Mathematics
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
| Hi-index | 5.23 |
We show that the l vertex disjoint paths problem between l pairs of vertices can be solved in linear time for co-graphs but is NP-complete for graphs of clique-width at most 6 and NLC-width at most 4. The NP-completeness follows from the fact that the line graph of a graph of tree-width k has clique-width at most 2k + 2 and NLC-width at most k + 2, and a result by Nishizeki et al. [The edge-disjoint paths problem is NP-complete for series-parallel graphs, Discrete Appl. Math. 115 (2001) 177-186]. The vertex disjoint paths problem is the first graph problem shown to be NP-complete on graphs of bounded clique-width but solvable in linear time on co-graphs and graphs of bounded tree-width. Additionally, we show that the r vertex disjoint paths problem between each of l pairs of vertices can be solved in polynomial time for co-graphs, if l is given to the input, and for graphs of bounded clique-width, if l is fixed.