  The percolation of Potts spins with equal values in Potts model on graphs
(networks) is considered. The general method for finding the Potts clusters
size distributions is developed. It allows for full description of percolation
transition when giant cluster of equal-valued Potts spins appears. The method
is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe
lattices with the arbitrary coordination number z. The analytical results for
the field-temperature percolation phase diagram of geometric spin clusters and
their size distribution are obtained. The last appears to be proportional to
that of the classical non-correlated bond percolation with the bond
probability, which depends on temperature and Potts model parameters.
