Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
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 threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The equivalence of theorem proving and the interconnection problem
ACM SIGDA Newsletter
Algorithmic construction of sets for k-restrictions
ACM Transactions on Algorithms (TALG)
Efficient approximation of convex recolorings
Journal of Computer and System Sciences
Convex recolorings of strings and trees: Definitions, hardness results and algorithms
Journal of Computer and System Sciences
The Complexity of Minimum Convex Coloring
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Convex Recoloring Revisited: Complexity and Exact Algorithms
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Speeding up dynamic programming for some NP-hard graph recoloring problems
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Partial convex recolorings of trees and galled networks: Tight upper and lower bounds
ACM Transactions on Algorithms (TALG)
Improved approximation algorithm for convex recoloring of trees
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Connected coloring completion for general graphs: algorithms and complexity
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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A coloring of the vertices of a graph is called convex if each subgraph induced by all vertices of the same color is connected. We consider three variants of recoloring a colored graph with minimal cost such that the resulting coloring is convex. Two variants of the problem are shown to be NP-hard on trees even if in the initial coloring each color is used to color only a bounded number of vertices. For graphs of bounded treewidth, we present a polynomial-time (2+@e)-approximation algorithm for these two variants and a polynomial-time algorithm for the third variant. Our results also show that, unless NP@?DTIME(n^O^(^l^o^g^l^o^g^n^)), there is no polynomial-time approximation algorithm with a ratio of size (1-o(1))lnlnN for the following problem: given pairs of vertices in an undirected N-vertex graph of bounded treewidth, determine the minimal possible number l for which all except l pairs can be connected by disjoint paths.