Graphs and Homomorphisms
Series: Oxford Graduate Texts in Mathematics;
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Product details:
- Edition number 2
- Publisher OUP Oxford
- Date of Publication 15 February 2026
- ISBN 9780198993414
- Binding Paperback
- No. of pages336 pages
- Size 234x156 mm
- Language English
- Illustrations 83 black & white figures 0
Categories
Short description:
Homomorphisms capture the dynamic aspects of networks and other structural models. The book includes most of the recent breakthroughs in this field, presenting the material from many different sources and developing the theory in an easily accessible form.
MoreLong description:
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.
Table of Contents:
Introduction
Products, retracts, and polymorphisms
The partial order of graphs and homomorphisms
The structure of composition
Testing for the existence of homomorphisms
Colouring: variations on a theme
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