  In "A survey on the Turaev genus of knots," Champanerkar and Kofman propose
several open questions. The first asks whether the polynomial whose
coefficients count the number of quasi-trees of the all-A ribbon graph obtained
from a diagram with minimal Turaev genus is an invariant of the knot. We answer
negatively by showing a counterexample obtained from the two diagrams of
$8_{21}$ on the KnotAtlas and KnotScape.
