Vertex disjoint equivalent subgraphs of order 3

Let k be a fixed integer at least 3. It is proved that every graph of order (2 k  − 1 − 1/ k ) n  +  O (1) contains n vertex disjoint induced subgraphs of order k suchthat these subgraphs are equivalent to each other and they are equivalent to one of four graphs: a clique, an independent set, a star, or the complement of a star. In particular, by substituting 3 for k , it is proved that every graph of order 14 n /3 +  O (1) contains n vertex disjoint induced subgraphs of order 3 such that they are equivalent to each other. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 159–166, 2007