  The three-state majority-vote model with noise on Erdos-Renyi's random graphs
has been studied. Using Monte Carlo simulations we obtain the phase diagram,
along with the critical exponents. Exact results for limiting cases are
presented, and shown to be in agreement with numerical values. We find that the
critical noise qc is an increasing function of the mean connectivity z of the
graph. The critical exponents beta/nu, gamma/nu and 1/nu are calculated for
several values of connectivity. We also study the globally connected network,
which corresponds to the mean-field limit z = N-1 -> infinity. Our numerical
results indicate that the correlation length scales with the number of nodes in
the graph, which is consistent with an effective dimensionality equal to unity.
