Parameterization and approximation are two popular ways of co** with NP-hard
problems. More recently, the two have also been combined to derive many interesting …

We introduce the notion of universal obstruction of a graph parameter, with respect to some
quasi-ordering relation. Universal obstructions may serve as compact characterizations of …

We introduce a graph-parametric framework for obtaining obstruction characterizations of
graph parameters with respect to partial ordering relations. For this, we define the notions of …

Let G and H be minor-closed graph classes. We say that the pair (H,\mathcalG) is an Erdös-
Pósa pair (EP-pair) if there exists a function f such that for every k and every graph G∈G …

What is the maximum number of copies of a fixed forest T in an n-vertex graph in a graph
class as? We answer this question for a variety of sparse graph classes. In particular, we …

We study the kernelization complexity of structural parameterizations of the Vertex Cover
problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce …

In 1986 Robertson and Seymour proved a generalization of the seminal result of Erd\H {o} s
and P\'osa on the duality of packing and covering cycles: A graph has the Erd\H {o} sP\'osa …

Let $ T $ be a tree on $ t $ vertices. We prove that for every positive integer $ k $ and every
graph $ G $, either $ G $ contains $ k $ pairwise vertex-disjoint subgraphs each having a $ T …

2k edges to obtain a triangle-free graph. The conjecture holds for graphs with small
treewidth or small maximum average degree, including planar graphs. However, for dense …

We study the kernelization complexity of structural parameterizations of the Vertex Cover
problem. Here, the goal is to find a polynomial-time preprocessing algorithm that can reduce …