This introductory chapter is a sampler of the material covered in the book. It introduces the notation and terminology in the book, and provides motivational examples and applications, many taken up in more detail in later chapters. It gives the flavour of combinatorial aspects, algorithmic aspects, retractions, duality, constraint satisfaction problems, as well as structural properties of homomorphism composition. The highlights of this chapter include a simple proof of the Colouring Interpolation Theorem, a generalization of the No-Homomorphism Lemma, the construction of a triangle-free graph to which all cubic triangle-free graphs are homomorphic, a case of the Edge Reconstruction Conjecture, and a generalization of a theorem of Frucht on graphs with prescribed automorphism groups.
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
If you think you should have access to this title, please contact your librarian.