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 …

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 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 …

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 …

An important question in the study of constraint satisfaction problems (CSP) is
understanding how the graph or hypergraph describing the incidence structure of the …

The main focus of this thesis is on using the divide and conquer technique to efficiently solve
graph problems that are in general intractable. We work in the field of parameterized …

Linear-width is a well-known and highly regarded graph parameter. The concept of Single
Ideal and Linear obstacle serves as an obstruction to linear-width on a connectivity sysem …

Branchwidth determines how graphs, and more generally, arbitrary connectivity (basically
symmetric and submodular) functions could be decomposed into a tree-like structure by …

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 …

This paper explores two fundamental concepts: branch width and weak ultrafilter. Branch
width is a significant graph width parameter that measures the degree of connectivity in a …