We present a method for reducing the treewidth of a graph while preserving all of its minimal
st separators up to a certain fixed size k. This technique allows us to solve st Cut and …

We obtain an algorithmic metatheorem for the following optimization problem. Let φ be a
counting monadic second order logic (CMSO) formula and t≧0 be an integer. For a given …

Vertex deletion and edge deletion problems play a central role in parameterized complexity.
Examples include classical problems like Feedback Vertex Set, Odd Cycle Transversal, and …

The Contractibility problem takes as input two graphs G and H, and the task is to decide
whether H can be obtained from G by a sequence of edge contractions. The Induced Minor …

Modifying a given graph to obtain another graph is a well-studied problem with applications
in many fields. Given two input graphs G and H, the Contractibility problem is to decide …

The Degree Contractibility problem is to test whether a given graph G can be modified to a
graph of minimum degree at least d by using at most k contractions. We prove the following …

A Note on Contracting Claw-Free Graphs Page 1 Discrete Mathematics and Theoretical
Computer Science DMTCS vol. 15:2, 2013, 223–232 A Note on Contracting Claw-Free Graphs …

The Induced Minor problem is that of testing whether a graph G can be modified into a graph
H by a sequence of vertex deletions and edge contractions. If only edge contractions are …

The Induced Minor problem is to test whether a graph G contains a graph H as an induced
minor, ie, if G can be modified into H by a sequence of vertex deletions and edge …

Abstract The H-Induced Minor Containment problem (H-IMC) consists in deciding if a fixed
graph H is an induced minor of a graph G given as input, that is, whether H can be obtained …