A b-matching of a graph is an assignment of non-negative integers to edges such that the sum at each node is at most a given bound. Its degree sequence is the vector whose components are the sums at each node. A linear-inequality description for the convex hull of degree sequences of b-matchings of a graph was found by Cunningham and Green-Krótki. This paper presents a polynomial-time combinatorial algorithm that either certifies a given vector as a member of the polyhedron or finds a valid inequality that is violated by the vector.
