  A connected graph has tree-depth at most $k$ if it is a subgraph of the
closure of a rooted tree whose height is at most $k$. We give an algorithm
which for a given $n$-vertex graph $G$, in time $\mathcal{O}(1.9602^n)$
computes the tree-depth of $G$. Our algorithm is based on combinatorial results
revealing the structure of minimal rooted trees whose closures contain $G$.
