  In the study of extensions of polytopes of combinatorial optimization
problems, a notorious open question is that for the size of the smallest
extended formulation of the Minimum Spanning Tree problem on a complete graph
with $n$ nodes. The best known lower bound is $\Omega(n^2)$, the best known
upper bound is $O(n^3)$.
  In this note we show that the venerable fooling set method cannot be used to
improve the lower bound: every fooling set for the Spanning Tree polytope has
size $O(n^2)$.
