  We study the Ising spin glass on random graphs with fixed connectivity z and
with a Gaussian distribution of the couplings, with mean \mu and unit variance.
We compute exact ground states by using a sophisticated branch-and-cut method
for z=4,6 and system sizes up to N=1280 for different values of \mu. We locate
the spin-glass/ferromagnet phase transition at \mu = 0.77 +/- 0.02 (z=4) and
\mu = 0.56 +/- 0.02 (z=6). We also compute the energy and magnetization in the
Bethe-Peierls approximation with a stochastic method, and estimate the
magnitude of replica symmetry breaking corrections. Near the phase transition,
we observe a sharp change of the median running time of our implementation of
the algorithm, consistent with a change from a polynomial dependence on the
system size, deep in the ferromagnetic phase, to slower than polynomial in the
spin-glass phase.
