A partial concentrator with parameters n,m, and c, is an n (inputs)×m (outputs) bipartite graph such that any set of k inputs, k•c, has a perfect matching to some set of k outputs. A partial concentrator is regular if each input has M edges and each output ahs nM/m edges. The authors study the probem of maximizing c for given m,n and M. For n=(m/M)2 Kufta and Vacroux, and Richards and Hwang, gave a similar construction of a partial concentrator and proved c≥M2+M-1. If, furthermore, m/M is a prime, the construction given by Richards and Hwang has a cyclic property. In this paper the authors use this cyclic property to prove c≥M2+2M-2. This is the best result possible for M=3 since it coincides with an upper bound previously proved.
