In this document, we present a covering problem where vertices of a graph have to be covered by rooted subtrees. We present three mixed-integer linear programming models, two of which are compact while the other is based on Dantzig-Wolfe decomposition. In the latter case, we focus on the column generation subproblem, for which we propose several algorithms. Numerical results are obtained using instances from the literature and instances based on a real-life districting application. Experiments show that the branch-and-price algorithm is able to solve much bigger instances than the compact model, which is limited to very small instance sizes.