6
Homomorphisms Lemma The chromatic number of a graph X is the least integer r such that there is a homomorphism from X to K r .
Homomorphisms
Lemma The chromatic number of a graph X is the least integer r such that there is a homomorphism from X to Kr .
Core
Lemma 6.2.1 Let X and Y be cores. Then X and Yare homomorphically equivalent il and only il they are isomorphic.
Lemma 6.2.2 Every graph has a core, which is an induced subgraph and is unique up to isomorphism.
Lemma 6.2.3 Two graphs X and Y are homomorphically equivalent if and only if their cores are isomorphic.
Products
All Contents from C. Godsil and G. Royle, Algebraic Graph Theory
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