The general Degree Sequence Problem asks for a simple undirected graph (that is a graph without self-loops and with no more than one edge between any pair of nodes) for which it holds that the degrees of the nodes are $D = (d_1, d_2, ..., d_n)$.

From the Erdős–Gallai theorem it follows that such a graph can be found in polynomial time. With some minor modifications it is also possible to ask for a simple undirected bi-partite graph for which it holds that the degrees of the nodes are $D_1 = (d_{1_1}, d_{1_2}, ..., d_{1_n})$ resp. $D_2 = (d_{2_1}, d_{2_2}, ..., d_{2_n})$.

I am interested in a more general case where the graph in question is a k-partite graph and the sets $D_1, D_2, ... D_k$ are given.

Is anybody aware of any results on that? I would suspect the problem to be NP-Hard but i don't (yet) have any proof.