Abstract
Let $\mathbf{D} = (X, D)$ be a Borel directed graph on a standard Borel space $X$ and let $\chi _B(\mathbf{D})$ be its Borel chromatic number. If $F_0, \ldots , F_{n-1}: X \to X$ are Borel functions, let $\mathbf{D}_{F_0, \ldots, F_{n-1}} $ be the directe
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