  In the 1970s, Gy\H{o}ri and Lov\'{a}sz showed that for a $k$-connected
$n$-vertex graph, a given set of terminal vertices $t_1, \dots, t_k$ and
natural numbers $n_1, \dots, n_k$ satisfying $\sum_{i=1}^{k} n_i = n$, a
connected vertex partition $S_1, \dots, S_k$ satisfying $t_i \in S_i$ and
$|S_i| = n_i$ exists. However, polynomial algorithms to actually compute such
partitions are known so far only for $k \leq 4$. This motivates us to take a
new approach and constrain this problem to particular graph classes instead of
restricting the values of $k$. More precisely, we consider $k$-connected
chordal graphs and a broader class of graphs related to them. For the first, we
give an algorithm with $O(n^2)$ running time that solves the problem exactly,
and for the second, an algorithm with $O(n^4)$ running time that deviates on at
most one vertex from the given required vertex partition sizes.
