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- Paul S. Bonsma, Luis Cereceda
- Theor. Comput. Sci.
- 2007

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)

- 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)

- Paul S. Bonsma, Florian Zickfeld
- LATIN
- 2008

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, Frederic Dorn
- ArXiv
- 2007

An out-branching of a directed graph is a rooted spanning tree with all arcs directed outwards from the root. We consider the problem of deciding whether a given digraph D has an out-branching with at least k leaves (Directed Spanning k-Leaf). We prove that this problem is fixed parameter tractable, when k is chosen as the parameter. Previously this was… (More)

- Paul S. Bonsma
- ArXiv
- 2010

- Paul S. Bonsma, Felix Breuer
- Algorithmica
- 2010

A hexagonal patch is a plane graph in which inner faces have length 6, inner vertices have degree 3, and boundary vertices have degree 2 or 3. We consider the following counting problem: given a sequence of twos and threes, how many hexagonal patches exist with this degree sequence along the outer face? This problem is motivated by the enumeration of… (More)

- Paul S. Bonsma, Nicola Ueffing, Lutz Volkmann
- Discrete Mathematics
- 2002

- Paul S. Bonsma
- Theor. Comput. Sci.
- 2012

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)

- Paul S. Bonsma, Jens Schulz, Andreas Wiese
- 2011 IEEE 52nd Annual Symposium on Foundations of…
- 2011

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)