Maximal Linear Arrangement is NP complete on Bipartite Graphs

The linear arrangement of a simple graph $G = (V,E)$ is a bijective labeling $π$ of the vertices of $G$ to the set $\{1, \ldots, n\}$. The maximum linear arrangement ($\texttt{maxLA}$) problem is to determine whether $G$ has a labeling such that the sum of labels across $G$'s edges, $\sum_{uv \in E}