  In a series of two preprints, Y.-P. Lee studied relations satisfied by all
formal Gromov-Witten potentials, as defined by A. Givental. He called them
"universal relations" and studied their connection with tautological relations
in the cohomology ring of moduli spaces of stable curves.
  Building on Y.-P. Lee's work, we give a simple proof of the fact that every
tautological relation gives rise to a universal relation (which was also proved
by Y.-P. Lee modulo certain results announced by C. Teleman).
  In particular, this implies that in any semi-simple Gromov-Witten theory
where arbitrary correlators can be expressed in genus 0 correlators using only
tautological relations, the formal and the geometric Gromov-Witten potentials
coincide.
  As the most important application, we show that our results suffice to deduce
the statement of a 1991 Witten conjecture on r-spin structures from the results
obtained by Givental for the corresponding formal Gromov-Witten potential.
  The conjecture in question states that certain intersection numbers on the
moduli space of r-spin structures can be arranged into a power series that
satisfies the r-KdV (or r-th higher Gelfand-Dikii) hierarchy of partial
differential equations.
