Marked Groups with Isomorphic Cayley Graphs but Different Borel Combinatorics
Logic
2019-06-03 v2
Abstract
We construct pairs of marked groups with isomorphic Cayley graphs but different Borel chromatic numbers for the free parts of their shift graphs. This answers a question of Kechris and Marks. We also show that these graphs have different Baire measurable and measure chromatic numbers, answering analogous versions of the question.
Keywords
Cite
@article{arxiv.1810.03062,
title = {Marked Groups with Isomorphic Cayley Graphs but Different Borel Combinatorics},
author = {Felix Weilacher},
journal= {arXiv preprint arXiv:1810.03062},
year = {2019}
}