  A proper 2-tone $k$-coloring of a graph is a labeling of the vertices with
elements from $\binom{[k]}{2}$ such that adjacent vertices receive disjoint
labels and vertices distance 2 apart receive distinct labels. The 2-tone
chromatic number of a graph $G$, denoted $\tau_2(G)$ is the smallest $k$ such
that $G$ admits a proper 2-tone $k$ coloring. In this paper, we prove that
w.h.p. for $p\ge Cn^{-1/4}\ln^{9/4}n$, $\tau_2(G_{n,p})=(2+o(1))\chi(G_{n,p})$
where $\chi$ represents the ordinary chromatic number. For sparse random graphs
with $p=c/n$, $c$ constant, we prove that $\tau_2(G_{n,p}) =
\lceil{{\sqrt{8\Delta+1} +5}/{2}}\rceil$ where $\Delta$ represents the maximum
degree. For the more general concept of $t$-tone coloring, we achieve similar
results.
