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Minimal definable graphs of definable chromatic number at least three (1906.08373v2)

Published 19 Jun 2019 in math.LO and math.CO

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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