M2M2-equipackable graphs

Let H   be a fixed graph. An HH-packing of G is a set of edge disjoint subgraphs of G each isomorphic to H  . An HH-packing in G with k   copies H1,H2,…,HkH1,H2,…,Hk of H is called maximal   if G-⋃i=1kE(Hi) contains no subgraph isomorphic to H  . An HH-packing in G with k   copies H1,H2,…,HkH1,H2,…,Hk of H is called maximum if no more than k edge disjoint copies of H can be packed into G. A graph G   is called HH-equipackable if every maximal H-packing in G   is also a maximum HH-packing in G  . By Mt,t⩾1Mt,t⩾1, we denote a matching having t   edges. In this paper, we investigate the characterization of M2M2-equipackable graphs.