Formula omitted]-equipackable graphs

Abstract

Let H be a fixed graph. An H - packing of G is a set of edge disjoint subgraphs of G each isomorphic to H. An H -packing in G with k copies H 1 , H 2 , … , H k of H is called maximal if G - ⋃ i = 1 k E ( H i ) contains no subgraph isomorphic to H. An H -packing in G with k copies H 1 , H 2 , … , H k 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 H - equipackable if every maximal H-packing in G is also a maximum H -packing in G. By M t , t ⩾ 1 , we denote a matching having t edges. In this paper, we investigate the characterization of M 2 -equipackable graphs.