Every branch of mathematics employs some notion of a product that enables the com-
bination or decomposition of its elemental structures. In graph theory there are four main …

Contains a wealth of information previously scattered in research journals, conference
proceedings and technical reports. Identifies more than 200 unsolved problems. Every …

This is a book about graph homomorphisms. Graph theory is now an established discipline
but the study of graph homomorphisms has only recently begun to gain wide acceptance …

Let H be a fixed graph, whose vertices are referred to as 'colors'. An H-coloring of a graph G
is an assignment of 'colors' to the vertices of G such that adjacent vertices of G obtain …

More than 30 years ago, Hedetniemi made a conjecture which says that the categorical
product of two n-chromatic graphs is still n-chromatic. The conjecture is still open, despite …

The theory of quasivarieties constitutes an independent direction in algebra and
mathematical logic and specializes in a fragment of first-order logic-the so-called universal …

Constraint satisfaction problems have enjoyed much attention since the early seventies, and
in the last decade have become also a focus of attention amongst theoreticians. Graph …

The core of a graph is its smallest subgraph which also is a homomorphic image. It turns out
the core of a finite graph is unique (up to isomorphism) and is also its smallest retract. We …

We provide a correspondence between the subjects of duality and density in classes of finite
relational structures. The purpose of duality is to characterise the structures C that do not …

The following problem, known as the H-colouring problem, is studied. An H-colouring of a
directed graph D is a mapping f:V(D)→V(H) such that (f(x),f(y)) is an edge of H whenever …