Tree-like continua do not admit expansive homeomorphisms

A homeomorphism $h:X \rightarrow X$ is called expansive provided that for some fixed $c >0$ and every $x,y \in X$ there exists an integer $n$, dependent only on $x$ and $y$, such that $d(h^n(x),h^n(y))>c$. It is shown that if $X$ is a tree-like continuum, then $h$ cannot be expansive.