  The zero-temperature Glauber dynamics is used to investigate the persistence
probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256,
512, 1024,4096,16384 $,..., $2^{30}$ states on {\it directed} and {\it
undirected} Barab\'asi-Albert networks and Erd\"os-R\'enyi random graphs. In
this model it is found that $P(t)$ decays exponentially to zero in short times
for {\it directed} and {\it undirected} Erd\"os-R\'enyi random graphs. For {\it
directed} and {\it undirected} Barab\'asi-Albert networks, in contrast it
decays exponentially to a constant value for long times, i.e, $P(\infty)$ is
different from zero for all $Q$ values (here studied) from $Q=3,4,5,...,
2^{30}$; this shows "blocking" for all these $Q$ values. Except that for
$Q=2^{30}$ in the {\it undirected} case $P(t)$ tends exponentially to zero;
this could be just a finite-size effect since in the other "blocking" cases you
may have only a few unchanged spins.
