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Randomized Borel (2d+1)-coloring of digraphs
Abstract
Let G be a Borel digraph with maximum out-degree d ∈ 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.
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BibTeX
@misc{bernshteyn2026randomized,
title = {{Randomized Borel $(2d+1)$-coloring of digraphs}},
author = {Anton Bernshteyn and Edward Hou and Forte Shinko and Felix Weilacher},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21286},
eprint = {2609.21286},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21286},
}
RIS
TY - UNPB
TI - Randomized Borel (2d+1)-coloring of digraphs
AU - Anton Bernshteyn
AU - Edward Hou
AU - Forte Shinko
AU - Felix Weilacher
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21286
UR - https://arxiv.org/abs/2609.21286
AB - Let G be a Borel digraph with maximum out-degree d ∈ 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.
ER -