Graphs and Homomorphisms

Graph theory and especially the study of graph homomorphisms has developed exponentially in the last couple of decades. Originally based on the authors’ graduate course lecture notes, this is still the only book devoted entirely to graph homomorphisms, bringing together the highlights of the theory and its many applications.

It offers a useful perspective on more traditional graph theory topics such as graph reconstruction, various forms of graph colouring, graph products, automorphism groups, chordality, and interval graphs, and has applications in complexity theory, artificial intelligence, telecommunication, and statistical physics. It is intended to be a sampler of this rich subject and focuses on its most interesting results, techniques, and applications, including its algebraic, combinatorial, and algorithmic aspects.

The book discusses most of the recent developments in the field, such as the disproof of the Hedetniemi Product Conjecture, the proof of the Feder-Vardi Dichotomy Conjecture of constraint satisfaction problems, as well as the celebrated theory of graph convergence and graphons. The text contains exercises of varying difficulty, intended to support readers’ learning and further development.

Pavol Hell, Professor Emeritus, School of Computing Science, Simon Fraser University, Jaroslav Nesetřil, Professor of Mathematics, Charles University

Pavol Hell is a Canadian mathematician and computer scientist, born in Czechoslovakia. He is a professor emeritus of computing science at Simon Fraser University. Hell obtained his PhD at the Université de Montreal, with Gert Sabidussi. He was a managing editor (2007-2021) of the Journal of Graph Theory and is a Fellow of the Society for Industrial and Applied Mathematics (SIAM) since 2012.

Jaroslav Nesetřil is professor of mathematics at Charles University in Prague. He received his Ph.D. from Charles University in 1973 under the supervision of Ales Pultr and Gert Sabidussi. Since 2006 he has been the chairman of the Czech National Committee for Mathematics. He is the Editor-In-Chief of Computer Science Review and of INTEGERS: The Electronic Journal of Combinatorial Number Theory and several other journals.