3-perfect hamiltonian decomposition of the complete graph

Abstract

Let n ≥ 5 be an odd integer and Kn the complete graph on n vertices. Let i be an integer with 2 ≤ i ≤ (n-1)/2. A hamiltonian decomposition H of Kn is called i-perfect if the set of the chords at distance i of the hamiltonian cycles in H is the edge