Preprocessing, or data reduction, is a standard technique for simplifying and speeding up
computation. Written by a team of experts in the field, this book introduces a rapidly …

We give an algorithm that, given an-vertex graph and an integer, in time either outputs a tree
decomposition of of width at most or determines that the treewidth of is larger than. This is …

In this paper we study quantum algorithms for NP-complete problems whose best classical
algorithm is an exponential time application of dynamic programming. We introduce the path …

We give an algorithm that takes as input an n-vertex graph G and an integer k, runs in time 2
O (k 2) n O (1), and outputs a tree decomposition of G of width at most k, if such a …

We continue the study of (tw, ω)-bounded graph classes, that is, hereditary graph classes in
which the treewidth can only be large due to the presence of a large clique, with the goal of …

We give a new general approach for designing exact exponential-time algorithms for subset
problems. In a subset problem the input implicitly describes a family of sets over a universe …

A hole in a graph is an induced cycle of length at least 4. A hole is long if its length is at least
5. By, we denote a path on vertices. In this paper, we give polynomial-time algorithms for the …

For a graph H, a graph G is an H-graph if it is an intersection graph of connected subgraphs
of some subdivision of H. H-graphs naturally generalize several important graph classes like …

For a tree decomposition $\mathcal {T} $ of a graph $ G $, by $\mu (\mathcal {T}) $ we
denote the size of a largest induced matching in $ G $ all of whose edges intersect one bag …

We study the tractability of the maximum independent set problem from the viewpoint of
graph width parameters, with the goal of defining a width parameter that is as general as …