Minimal definable graphs of definable chromatic number at least three
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-deg...
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Cambridge University Press
2021-01-01
|
Series: | Forum of Mathematics, Sigma |
Subjects: | |
Online Access: | https://www.cambridge.org/core/product/identifier/S2050509420000584/type/journal_article |
Summary: | 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. |
---|---|
ISSN: | 2050-5094 |