Packing of three copies of a graph

A graph of order n is said to be 3-placeable if there are three edge-disjoint copies of this graph in K_n. An (n, n − 1)-graph is a graph of order n with n − 1 edges. In this paper we characterize all the (n, n − 1)-graphs which contain no cycles of length 3 or 4 and which are 3-placeable. © 1996 John Wiley & Sons, Inc.