  Donald Knuth, in a draft of a coming volume of The Art of Computer
Programming, has recently conjectured that in Depth-First Search of a random
digraph with geometric outdegree distribution, the numbers of back and forward
arcs have the same distribution.
  We show that this conjecture is equivalent to an equality between two
generating functions defined by different recursions.
  Unfortunately, we have not been able so use this to prove the conjecture,
which still is open, but we hope that this note will inspire others to succeed
with the conjecture.
