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}
}
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. 

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