# Minimal definable graphs of definable chromatic number at least three

```@article{Carroy2019MinimalDG,
title={Minimal definable graphs of definable chromatic number at least three},
author={Rapha{\"e}l Carroy and Benjamin D. Miller and David Schrittesser and Zolt{\'a}n Vidny{\'a}nszky},
journal={Forum of Mathematics, Sigma},
year={2019},
volume={9}
}```
• Published 19 June 2019
• Mathematics
• Forum of Mathematics, Sigma
Abstract We show that there is a Borel graph on a standard Borel space of Borel chromatic number three that admits a Borel homomorphism to every analytic graph on a standard Borel space of Borel chromatic number at least three. Moreover, we characterize the Borel graphs on standard Borel spaces of vertex-degree at most two with this property and show that the analogous result for digraphs fails.
• Mathematics
ArXiv
• 2021
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• Mathematics
Inventiones mathematicae
• 2021
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