Graph minors. VI. Disjoint paths across a disc
Journal of Combinatorial Theory Series B
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Graph minors. VII. Disjoint paths on a surface
Journal of Combinatorial Theory Series B
Easy problems for tree-decomposable graphs
Journal of Algorithms
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An algebraic theory of graph reduction
Journal of the ACM (JACM)
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Efficient parallel algorithms for graphs of bounded tree-width
Journal of Algorithms
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Generation of a Linear Time Query Processing Algorithm Based on Well-Quasi-Orders
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Parameterized complexity of discrete morse theory
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We present a modification of Bodlaender's linear time algorithm that, for constant k, determines whether an input graph G = (V, E) has treewidth k and, if so, constructs a tree decomposition of G of width at most k. Our algorithm has the following additional feature: if G has treewidth greater than k then a subgraph G′ of G of treewidth greater than k is returned along with a tree decomposition of G′ of width at most 2k. A consequence is that the fundamental disjoint rooted paths problem can now be solved in O(n2) time. This is the primary motivation for this paper.