CaltechAUTHORS: Article
https://feeds.library.caltech.edu/people/Vidnyánszky-Zoltán/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 08 Nov 2024 19:27:05 -0800Minimal definable graphs of definable chromatic number at least three
https://resolver.caltech.edu/CaltechAUTHORS:20210304-150950107
Year: 2021
DOI: 10.1017/fms.2020.58
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.https://resolver.caltech.edu/CaltechAUTHORS:20210304-150950107A complexity problem for Borel graphs
https://resolver.caltech.edu/CaltechAUTHORS:20210514-103015736
Year: 2021
DOI: 10.1007/s00222-021-01047-z
We show that there is no simple (e.g. finite or countable) basis for Borel graphs with infinite Borel chromatic number. In fact, it is proved that the closed subgraphs of the shift graph on [N]^N with finite (or, equivalently, ≤3) Borel chromatic number form a Σ1/2-complete set. This answers a question of Kechris and Marks and strengthens several earlier results.https://resolver.caltech.edu/CaltechAUTHORS:20210514-103015736The structure of random automorphisms of the random graph
https://resolver.caltech.edu/CaltechAUTHORS:20220607-425364000
Year: 2022
DOI: 10.1016/j.apal.2022.103152
We give a complete description of the size of the conjugacy classes of the automorphism group of the random graph with respect to Christensen's Haar null ideal. It is shown that every non-Haar null class contains a translated copy of a nonempty portion of every compact set and that there are continuum many non-Haar null conjugacy classes. Our methods also yield a new proof of an old result of Truss.https://resolver.caltech.edu/CaltechAUTHORS:20220607-425364000