  Alon and Wormald showed that any graph with minimum degree d contains a
spanning star forest in which every connected component is of size at least
\Omega((d/\log d)^{1/3}). They asked if any connected graph with minimum degree
at least d has a spanning tree in which every internal vertex has degree at
least cd/\log d, for some absolute constant c > 0.
  We give a simple example showing that this is not the case.
