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math.LO2021
On Homomorphism Graphs
Sebastian Brandt, Yi-Jun Chang, Jan Grebík +3
We introduce a new type of examples of bounded degree acyclic Borel graphs and study their combinatorial properties in the context of descriptive combinatorics, using a generalizat…
math.LO2021
Approximate Schreier decorations and approximate Kőnig's line coloring Theorem
Jan Grebik
Following recent result of L. M. T\' oth [arXiv:1906.03137] we show that every -regular Borel graph with a (not necessarily invariant) Borel probability measure a…
math.CO2021
Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics
Sebastian Brandt, Yi-Jun Chang, Jan Grebík +3
We study connections between distributed local algorithms, finitary factors of iid processes, and descriptive combinatorics in the context of regular trees. We extend the Borel det…