  The conjecture of Peter Horak and Alex Rosa (generalizing that of Marco
Buratti) states that a multiset L of v-1 positive integers not exceeding [v/2]
is the list of edge-lengths of a suitable Hamiltonian path of the complete
graph with vertex-set {0,1,...,v-1} if and only if the following condition
(here reformulated in a slightly easier form) is satisfied: for every divisor d
of v, the number of multiples of d appearing in L is at most v-d. In this paper
we do some preliminary discussions on the conjecture, including its
relationship with graph decompositions. Then we prove, as main result, that the
conjecture is true whenever all the elements of L are in {1,2,3,5}.
