Consider a bipartite Garph $ G=(L \cup R, E)$ . Naturally, a b-Matching problem is to find a set of edges $ M \subset E$ , such that each node in $ L$ and $ R$ are adjuscent to maximum $ b$ neighbors, and a weight function $ w(e), e \in E$ is maximized. What if we have different $ b$ ? e.g., $ b(v)=5, \forall v \in R$ and $ b(v)=2, \forall v \in L$ . How do you call the problem? Is is constrained matching, or k-cardinality assignment, or what? I need to find some literature for it.

Thanks!