  Two vertices $u, v \in V$ of an undirected connected graph $G=(V,E)$ are
resolved by a vertex $w$ if the distance between $u$ and $w$ and the distance
between $v$ and $w$ are different. A set $R \subseteq V$ of vertices is a
$k$-resolving set for $G$ if for each pair of vertices $u, v \in V$ there are
at least $k$ distinct vertices $w_1,\ldots,w_k \in R$ such that each of them
resolves $u$ and $v$. The $k$-Metric Dimension of $G$ is the size of a smallest
$k$-resolving set for $G$. The decision problem $k$-Metric Dimension is the
question whether G has a $k$-resolving set of size at most $r$, for a given
graph $G$ and a given number $r$. In this paper, we proof the NP-completeness
of $k$-Metric Dimension for bipartite graphs and each $k \geq 2$.
