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arXiv · 1906.08373

Minimal definable graphs of definable chromatic number at least three

Raphael Carroy·Benjamin D. Miller·David Schrittesser·Zoltan Vidnyanszky
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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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Raphael Carroy, Benjamin D. Miller, David Schrittesser, Zoltan Vidnyanszky. 2019-06-19. Minimal definable graphs of definable chromatic number at least three. https://doi.org/10.1017/fms.2020.58

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