  We extend the theory of minimal absent words to (rooted and unrooted) trees,
having edges labeled by letters from an alphabet $\Sigma$ of cardinality
$\sigma$. We show that the set $\text{MAW}(T)$ of minimal absent words of a
rooted (resp. unrooted) tree $T$ with $n$ nodes has cardinality $O(n\sigma)$
(resp. $O(n^{2}\sigma)$), and we show that these bounds are realized. Then, we
exhibit algorithms to compute all minimal absent words in a rooted (resp.
unrooted) tree in output-sensitive time $O(n+|\text{MAW}(T)|)$ (resp.
$O(n^{2}+|\text{MAW}(T)|)$ assuming an integer alphabet of size polynomial in
$n$.
