Path coverings with paths

In this paper, we give two new proofs of a result of Heinrich, Langdeau and Verrall that provide necessary and sufficient conditions for the existence of a set S of 3-paths in K-n having the property that each 2-path in K-n l ies in exactly one path in S. These are then used to consider the case n=3 (mod 4) when no such exact covering is possible, and to solve the problem o f covering (k-1)-paths with k-paths for all k greater than or equal to 3. ( C) 2001 John Wiley & Sons. Inc.