  Glauber dynamics of a bond-diluted Ising model on a Bethe lattice (a random
graph with fixed connectivity) is investigated by an approximate theory which
provides exact results for equilibrium properties. The time-dependent solutions
of the dynamical system derived by this method are in good agreement with the
results obtained by Monte Carlo simulations in almost all situations.
Furthermore, the derived dynamical system exhibits a remarkable phenomenon that
the magnetization shows multi-step relaxations at intermediate time scales in a
low-temperature part of the Griffiths phase without bond percolation clusters.
