521 research outputs found
Distinguishing homomorphisms of infinite graphs
We supply an upper bound on the distinguishing chromatic number of certain
infinite graphs satisfying an adjacency property. Distinguishing proper
-colourings are generalized to the new notion of distinguishing
homomorphisms. We prove that if a graph satisfies the connected
existentially closed property and admits a homomorphism to , then it admits
continuum-many distinguishing homomorphisms from to join
Applications are given to a family universal -colourable graphs, for a
finite core
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