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Homomorphisms

  • Chris Godsil
  • Gordon Royle
Part of the Graduate Texts in Mathematics book series (GTM, volume 207)

Abstract

Although any isomorphism between two graphs is a homomorphism, the study of homomorphisms between graphs has quite a different flavour to the study of isomorphisms. In this chapter we support this claim by introducing a number of topics involving graph homomorphisms. We consider the relationship between homomorphisms and graph products, and in particular a famous unsolved conjecture of Hedetniemi, which asserts that if two graphs are not n-colourable, then neither is their product. Our second major topic is the exploration of the core of a graph, which is the minimal subgraph of a graph that is also a homomorphic image of the graph. Studying graphs that are equal to their core leads us to an interesting class of graphs first studied by Andrásfai. We finish the chapter with an exploration of the cores of vertex-transitive graphs.

Keywords

Connected Graph Chromatic Number Cayley Graph Common Neighbour Petersen Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Chris Godsil
    • 1
  • Gordon Royle
    • 2
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Department of Computer ScienceUniversity of Western AustraliaNedlandsAustralia

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