  For all integers $k\geq 3$, we give an $O(n^4)$ time algorithm for the
problem whose instance is a graph $G$ of girth at least $k$ together with $k$
vertices and whose question is "Does $G$ contains an induced subgraph
containing the $k$ vertices and isomorphic to a tree?". This directly follows
for $k=3$ from the three-in-a-tree algorithm of Chudnovsky and Seymour and for
$k=4$ from a result of Derhy, Picouleau and Trotignon. Here we solve the
problem for $k\geq 5$. Our algorithm relies on a structural description of
graphs of girth at least $k$ that do not contain an induced tree covering $k$
given vertices ($k\geq 5$).
