
TL;DR
The paper constructs a smooth locally finite Borel graph with a local coloring problem that admits a solution but cannot be realized as a Borel coloring, highlighting limitations of Borel methods.
Contribution
It demonstrates the existence of a smooth locally finite Borel graph with a local coloring problem solvable in theory but not via Borel coloring, revealing new limitations.
Findings
Existence of a smooth locally finite Borel graph with a solvable local coloring problem.
Such a graph admits a coloring solving the problem but no Borel coloring exists.
Highlights limitations of Borel methods in graph coloring problems.
Abstract
We construct a smooth locally finite Borel graph and a local coloring problem such that has a coloring that solves , but no such coloring can be Borel.
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