The survey is a comprehensive overview of the develo** area of parameterized
algorithms for graph modification problems. It describes state of the art in kernelization …

The goal of this textbook is twofold. First, the book serves as an introduction to the field of
parameterized algorithms and complexity accessible to graduate students and advanced …

Given an undirected graph G, a collection (s1, t1),...,(sl, tl) of pairs of vertices, and an integer
p, the Edge Multicut problem ask if there is a set S of at most p edges such that the removal …

A directed odd cycle transversal of a directed graph (digraph) D is a vertex set S that
intersects every odd directed cycle of D. In the Directed Odd Cycle Transversal (DOCT) …

Given a graph G and an integer k, the Feedback Vertex Set (FVS) problem asks if there is a
vertex set T of size at most k that hits all cycles in the graph. The first fixed-parameter …

In the Subset Feedback Vertex Set (Subset FVS) problem, the input is a graph G on n
vertices and m edges, a subset of vertices T, referred to as terminals, and an integer k. The …

Planarity, bipartiteness and (directed) acyclicity are basic graph properties with classic linear
time recognition algorithms. However, the problems of testing whether a given (di) graph has …

In the deletion version of the list homomorphism problem, we are given graphs G and H, a
list L (v) ⊆ V (H) L (v)⊆ V (H) for each vertex v ∈ V (G) v∈ V (G), and an integer k. The task …

The Constraint Satisfaction Problem (CSP) is a central and generic computational problem
which provides a common framework for many theoretical and practical applications. A …

We present two new combinatorial tools for the design of parameterized algorithms. The first
is a simple linear time randomized algorithm that given as input ad-degenerate graph G and …