## 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!

## Algorithm for b-matching on bipartite graph [duplicate]

I have a bipartite graph, where I want to assign nodes in Left set to Right set of nodes. There is a “b” constraint, which limits the maximum possible node degrees on the Right set. Since it is a classic problem, I expected to find a lot of algorithms on it, but was not successful. Any ideas how to solve it?