  A harmonious coloring of $G$ is a proper vertex coloring of $G$ such that
every pair of colors appears on at most one pair of adjacent vertices. The
harmonious chromatic number of $G$, $h(G)$, is the minimum number of colors
needed for a harmonious coloring of $G$. We show that if $T$ is a forest of
order $n$ with maximum degree $\Delta(T)\geq \frac{n+2}{3}$, then $$h(T)=
  \Delta(T)+2, & if $T$ has non-adjacent vertices of degree $\Delta(T)$;
  \Delta(T)+1, & otherwise.
  $$ Moreover, the proof yields a polynomial-time algorithm for an optimal
harmonious coloring of such a forest.
