Minimal definable graphs of definable chromatic number at least three
Logic
2022-10-11 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1906.08373,
title = {Minimal definable graphs of definable chromatic number at least three},
author = {Raphael Carroy and Benjamin D. Miller and David Schrittesser and Zoltan Vidnyanszky},
journal= {arXiv preprint arXiv:1906.08373},
year = {2022}
}