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arXiv · 1309.0416

Distinguishing homomorphisms of infinite graphs

Anthony Bonato·Dejan Delic
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Abstract

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 $K_2.$ Applications are given to a family universal $H$-colourable graphs, for $H$ a finite core.

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Anthony Bonato, Dejan Delic. 2013-09-02. Distinguishing homomorphisms of infinite graphs. https://arxiv.org/abs/1309.0416

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