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Marked groups with isomorphic Cayley graphs but different Borel combinatorics

Volume 251 / 2020

Felix Weilacher 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.


  • Felix WeilacherCarnegie Mellon University
    5000 Forbes Ave
    Pittsburgh, PA 15213, U.S.A.

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