  A simple model of cyclically competing species on a directed graph with
quenched disorder is proposed as an extension of the rock-paper-scissors model.
By assuming that the effects of loops in a directed random graph can be ignored
in the thermodynamic limit, it is proved for any finite disorder that the
system fixates to a frozen configuration when the species number $s$ is larger
than the spatial connectivity $c$, and otherwise stays active. Nontrivial lower
and upper bounds for the persistence probability of a site never changing its
state are also analytically computed. The obtained bounds and numerical
simulations support the existence of a phase transition as a function of
disorder for $1<c_l(s)\le c <s$, with a $s$-dependent threshold of the
connectivity $c_l(s)$.
