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 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 …

The study of circular chromatic number Xc (G) of a graph G, which is a refinement of its
chromatic number, has been very active in the past decade. Many nice results are obtained …

What is the chromatic number of the product of two graphs? The conjecture of Hedetniemi
(Hedetniemi, University of Michigan Technical Report 0315-44-7, 1966), which is more than …

The chromatic number of G× H can be less than the minimum of the chromatic numbers of
finite simple graphs G and H. The tensor product G× H of finite simple graphs G and H has …

In this article we survey the emerging field of descriptive graph combinatorics. This area has
developed in the last two decades or so at the interface of descriptive set theory and graph …

The approximate graph coloring problem, whose complexity is unresolved in most cases,
concerns finding a-coloring of a graph that is promised to be-colorable, where. This problem …

We present new results on approximate colourings of graphs and, more generally,
approximate H-colourings and promise constraint satisfaction problems. First, we show NP …

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 …

This paper proves that the fractional version of Hedetniemi's conjecture is true. Namely, for
any graphs G and H, χf (G× H)= min {χf (G), χf (H)}. As a by-product, we obtain a proof of the …