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 …

We present an intimate connection among the following fields:(a) distributed local
algorithms: coming from the area of computer science,(b) finitary factors of iid processes …

The theory of definable equivalence relations has been a very active area of research in
descriptive set theory during the last three decades. It serves as a foundation of a theory of …

In this paper we consider coloring problems on graphs and other combinatorial structures on
standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings …

We provide a gentle introduction, aimed at non-experts, to Borel combinatorics that studies
definable graphs on topological spaces. This is an emerging field on the borderline between …

We show that every Borel graph $ G $ of subexponential growth has a Borel proper edge-
coloring with $\Delta (G)+ 1$ colors. We deduce this from a stronger result, namely that an …

We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ+
1)-edge-coloring of an n-vertex graph of maximum degree Δ in poly (Δ, log⁡ n) rounds. This …

Odd Distances in Colourings of the Plane | Geometric and Functional Analysis Skip to main
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We establish two versions of Vizing's theorem for Borel multi-graphs whose vertex degrees
and edge multiplicities are uniformly bounded by respectively Δ and π. The “approximate” …

Extremal aspects of graph and hypergraph decomposition problems. Page 245 Extremal aspects
of graph and hypergraph decomposition problems Stefan Glock Daniela Kühn Deryk Osthus …