Restricted b-matchings in degree-bounded graphs

We present a min-max formula and a polynomial time algorithm for a slight generalization of the following problem: in a simple undirected graph in which the degree of each node is at most t + 1, find a maximum t-matching containing no member of a list of forbidden K t,t and K t + 1 subgraphs. An analogous problem for bipartite graphs without degree bounds was solved by Makai [15], while the special case of finding a maximum square-free 2-matching in a subcubic graph was solved in [1].