The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Edge-disjoint paths in a grid bounded by two nested rectangles
Discrete Applied Mathematics - Computational combinatiorics
Easy problems for tree-decomposable graphs
Journal of Algorithms
On the complexity of finding iso- and other morphisms for partial k-trees
Discrete Mathematics - Topological, algebraical and combinatorial structures; Froli´k's memorial volume
An algebraic theory of graph reduction
Journal of the ACM (JACM)
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
NP-completeness of some edge-disjoint paths problems
Discrete Applied Mathematics
Approximations for the disjoint paths problem in high-diameter planar networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
The complexity of subgraph isomorphism for classes of partial k-trees
Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Finding Edge-Disjoint Paths in Partial k-Trees (Extended Abstract)
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Faster Algorithms for Subgraph Isomorphism of k-Connected Partial k-Trees
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth
Proceedings of the forty-second ACM symposium on Theory of computing
Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth
Journal of the ACM (JACM)
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Many combinatorial problems are NP-complete for general graphs, but are not NP-complete for partial k-trees (graphs of treewidth bounded by a constant k) and can be efficiently solved in polynomial time or mostly in linear time for partial k-trees. On the other hand, very few problems are known to be NP-complete for partial k-trees with bounded k. These include the subgraph isomorphism problem and the bandwidth problem. However, all these problems are NP-complete even for ordinary trees or forests. In this paper we show that the edge-disjoint paths problem is NP-complete for partial k-trees with some bounded k, say k = 3, although the problem is trivially solvable for trees.