  A graph $G$ is called a replication graph of a graph $H$ if $G$ is obtained
from $H$ by replacing vertices of $H$ by arbitrary cliques of vertices and then
replacing each edge in $H$ by all the edges between corresponding cligues. For
a given graph $H$ the $\rho_R(H)$ is the minimal number of vertices of a
replication graph $G$ of $H$ such that every proper vertex coloring of $G$
contains a rainbow induced subgraph isomorphic to $H$ having exactly one vertex
in each replication clique of $G$. We prove some bounds for $\rho_R$ for some
classes of graphs and compute some exact values. Also some experimental results
obtained by a computer search are presented and conjectures based on them are
formulated.
