  Let $S=\mathbb{K}[x_1,\dots, x_n]$ be a polynomial ring, where $\mathbb{K}$
is a field, and $G$ be a simple graph on $n$ vertices. Let $J(G)\subset S$ be
the vertex cover ideal of $G$. Herzog, Hibi and Ohsugi have conjectured that
all powers of vertex cover ideals of chordal graph are componentwise linear.
Here we establish the conjecture for the special case of trees. We also show
that if $G$ is a unicyclic vertex decomposable graph that does not contain
$C_3$ or $C_5$, then symbolic powers of $J(G)$ are componentwise linear.
