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 K 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].

Bibtex entry:

@techreport{egres-09-12,

AUTHOR | = | {B{\'e}rczi, Krist{\'o}f and V{\'e}gh, L{\'a}szl{\'o}}, |

TITLE | = | {Restricted b-matchings in degree-bounded graphs}, |

NOTE | = | {{\tt www.cs.elte.hu/egres}}, |

INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |

YEAR | = | {2009}, |

NUMBER | = | {TR-2009-12} |