Parameterized complexity/multivariate complexity algorithmics is an exciting field of modern
algorithm design and analysis, with a broad range of theoretical and practical aspects that …

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 …

For a positive integer k, ak‐coloring of a graph is a map** such that whenever. The
Coloring problem is to decide, for a given G and k, whether ak‐coloring of G exists. If k is …

In a parameterized problem, every instance I comes with a positive integer k. The problem is
said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the …

We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed
graph H as a minor to graphs excluding H as a topological subgraph. We prove that for a …

The aim of this article is to motivate and describe the parameter ecology program, which
studies how different parameters contribute to the difficulty of classical problems. We call for …

Given two graphs $ H $ and $ G $, the Subgraph Isomorphism problem asks if $ H $ is
isomorphic to a subgraph of $ G $. While NP-hard in general, algorithms exist for various …

The grid theorem, originally proved in 1986 by Robertson and Seymour in Graph Minors V,
is one of the most central results in the study of graph minors. It has found numerous …

In the classic Minimum Bisection problem we are given as input a graph G and an integer k.
The task is to determine whether there is a partition of V (G) into two parts A and B such that …

Given a graph G and k pairs of vertices (s 1, t 1),...,(sk, tk), the k-Vertex-Disjoint Paths
problem asks for pair wise vertex-disjoint paths P 1,..., Pk such that Pi goes from si to ti …