The existence of a polynomial kernel for Odd Cycle Transversal was a notorious open
problem in parameterized complexity. Recently, this was settled by the present authors …

A recent trend in parameterized algorithms is the application of polytope tools to fixed-
parameter tractable (FPT) algorithms eg, Cygan et al., FOCS 2011, 52nd Annual Symposium …

We continue the development of matroid-based techniques for kernelization, initiated by the
present authors [47]. We significantly extend the usefulness of matroid theory in …

Several min–max relations in graph theory can be expressed in the framework of the Erdős–
Pósa property. Typically, this property reveals a connection between packing and covering …

A Kl-expansion consists of l vertex-disjoint trees, every two of which are joined by an edge.
We call such an expansion odd if its vertices can be two-coloured so that the edges of the …

We study the parameterized complexity of several vertex-and edge-deletion problems on
graphs, parameterized by the number p of deletions. The first kind of problems are …

Abstract A (Γ 1, Γ 2)-labeled graph is an oriented graph with its edges labeled by elements
of the direct sum of two groups Γ 1, Γ 2. A cycle in such a labeled graph is (Γ 1, Γ 2)-non-zero …

A classic theorem of Erdős and Pósa states that there exists a constant c such that for all
positive integers k and graphs G, either G contains k vertex disjoint cycles, or there exists a …

We consider the following problem, which is called the odd cycles transversal problem.
Input: A graph G and an integer k. Output: A vertex set X∊ V (G) with| X|≤ k such that G–X is …

This thesis is about a conjecture of Geelen on the structure of graphs with a forbidden vertex-
minor; the conjecture is like the Graph Minors Structure Theorem of Robertson and Seymour …