“…Some of the most studied graph partitioning problems are those with a cardinality constraint on the number of components. These problems are NP-hard on arbitrary graphs, but, in many cases, they can be solved in polynomial time on trees (see, e.g., [3,6,8,13,17,25]). Polynomial time algorithms are also known for the max-split clustering problem on ladder graphs [26], and, more generally, on outerplanar graphs [28], as well as for equipartition problems on ladder graphs [7].…”