Paul S. Bonsma

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Suppose we are given a graph G together with two proper vertex k-colourings of G, α and β. How easily can we decide whether it is possible to transform α into β by recolouring vertices of G one at a time, making sure we always have a proper k-colouring of G? This decision problem is trivial for k = 2, and decidable in polynomial time for k = 3. Here we(More)
In this paper, we present a constant-factor approximation algorithm for the unsplittable flow problem on a path. This improves on the previous best known approximation factor of O(log n). The approximation ratio of our algorithm is 7+e for any e>0. In the unsplittable flow problem on a path, we are given a capacitated path P and n tasks, each task(More)
The Shortest Path Reconfiguration problem has as input a graph G with unit edge lengths, with vertices s and t, and two shortest st-paths P and Q. The question is whether there exists a sequence of shortest st-paths that starts with P and ends with Q, such that subsequent paths differ in only one vertex. This is called a rerouting sequence. This problem is(More)
We study the following independent set reconfiguration problem, called TAR-Reachability: given two independent sets I and J of a graph G, both of size at least k, is it possible to transform I into J by adding and removing vertices one-by-one, while maintaining an independent set of size at least k throughout? This problem is known to be PSPACE-hard in(More)
A rerouting sequence is a sequence of shortest st-paths such that consecutive paths differ in one vertex. We study the Shortest Path Rerouting Problem, which asks, given two shortest st-paths P and Q in a graph G, whether a rerouting sequence exists from P to Q. This problem is PSPACE-hard in general, but we show that it can be solved in polynomial time if(More)
Let G be a graph with vertex set V (G) and edge set E(G). For X ⊆ V (G) let G[X ] be the subgraph induced by X , 7 X = V (G) − X , and (X; 7 X ) the set of edges in G with one end in X and the other in 7 X . If G is a connected graph and S ⊂ E(G) such that G − S is disconnected, and each component of G − S consists of at least three vertices, then we speak(More)
In the first part of this work we study the following question: Given two k-colorings α and β of a graph G on n vertices and an integer , can α be modified into β by recoloring vertices one at a time, while maintaining a k-coloring throughout and using at most such recoloring steps? This problem is weakly PSPACE-hard for every constant k ≥ 4. We show that(More)