  The shift graph is defined on the space of infinite subsets of natural
numbers by letting two sets be adjacent if one can be obtained from the other
by removing its least element. We show that this graph is not a minimum among
the graphs of the form $G_{f}$ defined on some Polish space $X$, where two
distinct points are adjacent if one can be obtained from the other by a given
Borel function $f:X\to X$. This answers the primary outstanding question from
\cite{Kechris19991}.
