**Erratum -- Jump operations for Borel graphs**

In the first paragraph of Section 3 of the paper, we say that if $G^*$ has a cyclce of length $n$, then $G$ has a cycle of length $n$. For this to be true, we need to assume that $n$ is odd. This error doesn't impact any of the theorems or proofs of the paper (which only use this observation when $n$ is odd). Thanks to Kirill Gura for pointing out this error!