Analysis reports an upper bound on distinguishing chromatic number of infinite graphs, suggesting implications for homomorphisms.
We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper n-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph G satisfies the connected existentially closed property and admits a homomorphism to H, then it admits continuum-many distinguishing homomorphisms from G to H join K2. Applications are given to a family universal H-colourable graphs, for H a finite core.
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Bonato et al. (2012) studied this question.
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