# Is there such a problem as b-Matching with different b values?

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!