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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)

We study the unsplittable flow problem on a path P. We are given a set of n tasks. Each task is specified by a sub path of P , a demand, and a profit. Moreover, each edge of P has a given capacity. The aim is to find a subset of the tasks with maximum profit, for which the given demands can be simultaneously routed along P , subject to the capacities. The… (More)

- Paul S. Bonsma
- WG
- 2014

We study the following independent set reconfiguration problem, called TAR-Reachabi-lity: 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)

It is known that graphs on n vertices with minimum degree at least 3 have spanning trees with at least n/4 + 2 leaves and that this can be improved to (n + 4)/3 for cubic graphs without the diamond K 4 − e as a subgraph. We generalize the second result by proving that every graph with minimum degree at least 3, without diamonds and certain subgraphs called… (More)

- Paul S Bonsma, W H M Zijm, Ir J P M Van Den Heuvel, H L Kratsch, E C Bodlaender, Van Berkum +1 other
- 2006

The graph shown on the cover of this thesis is one of the graphs used in the N P-completeness proofs of Chapter 3. The bold edges indicate a matching-cut in this graph, consisting of two of the six minimal matching-cuts possible in this graph. The cut consisting of the eleven dashed edges separates the graph into two parts with 56 vertices. This is a… (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 present a polynomial-time algorithm that given two independent sets in a claw-free graph G decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex v from the current independent set S in the sequence and to add a new vertex w (not in S) such that the set S −v +w is independent in… (More)