Marked groups with isomorphic Cayley graphs but different Borel combinatorics
Volume 251 / 2020
Fundamenta Mathematicae 251 (2020), 69-86 MSC: Primary 03E15. DOI: 10.4064/fm863-2-2020 Published online: 20 March 2020
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.