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 …

The study of graph structure has advanced in recent years with great strides: finite graphs
can be described algebraically, enabling them to be constructed out of more basic elements …

A contraction sequence of a graph consists of iteratively merging two of its vertices until only
one vertex remains. The recently introduced twin-width graph invariant is based on …

We show that determining if an $ n $-vertex graph has twin-width at most 4 is NP-complete,
and requires time $2^{\Omega (n/\log n)} $ unless the Exponential-Time Hypothesis fails …

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

Quantum communication between distant parties is based on suitable instances of shared
entanglement. For efficiency reasons, in an anticipated quantum network beyond point-to …

In this survey, we review practical algorithms for graph-theoretic problems that are
expressible in monadic second-order logic. Monadic second-order (MSO) logic allows …

Graph characteristics are often analyzed through various parameters, with ongoing research
dedicated to exploring these aspects. A hypergraph is a generalization of the conventional …

Graph characteristics are often analyzed through various parameters, with ongoing research
dedicated to exploring these aspects. A hypergraph is a generalization of the conventional …

We introduce the notion of delineation. A graph class $\mathcal C $ is said delineated if for
every hereditary closure $\mathcal D $ of a subclass of $\mathcal C $, it holds that $\mathcal …