English

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}
}
R2 v1 2026-06-23T04:30:50.566Z