Optimal packing of induced stars in a graph

We consider simple undirected graphs. An edge subset A of C is called an induced n-star packing of G if every component of the subgraph G[A] induced by A is a star with at most n edges and is an induced subgraph of G. We consider the problem of finding an induced n-star packing of G that covers the maximum number of vertices. This problem is a natural generalization of the classical matching problem. We show that many classical results on matchings (such as the Tutte 1-Factor Theorem, the Berge Duality Theorem, the Gallai-Edmonds Structure Theorem, the Matching Matroid Theorem) can be extended to induced n-star packings in a graph.