Work

Randomized Borel $(2d+1)$-coloring of digraphs

Year: 2026

Type: preprint

Abstract: Let $G$ be a Borel digraph with maximum out-degree $d \in \mathbb{N}$. We show that $G$ admits a random Borel $(2d+1)$-coloring for which every edge is almost surely not monochromatic. This gives a simpler proof of a recent result of Pelayo-Gómez: such a graph $G$ admits a measurable proper $(2d+1)$-coloring with respect to any Borel probability measure on $V(G)$. Our proof is an adaptation of Pelayo-Gómez's proof to the randomized Borel setting.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.21286

Authors: Bernshteyn, Anton, Hou, Edward, Shinko, Forte, Weilacher, Felix

Institution: University of California, Los Angeles

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation

Awards: CAREER: Developing a unified theory of descriptive combinatorics and local algorithms, G6671297155, Postdoctoral Fellowship: MSPRF: Definable Combinatorics in Descriptive Set Theory, Computability Theory, and Beyond

OpenAlex ID: W7213866158

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