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 …

This text is aimed at doctoral students and researchers, who are interested in Combinatorics
and Graph Theory or who would just like to learn about some active topics and trends. But …

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 …

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 …

In a nutshell, a duality for a constraint satisfaction problem equates the existence of one
homomorphism to the non-existence of other homomorphisms. In this survey paper, we give …

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 …