Sách Hamiltonian paths in the complete graph with edge-lengths 1, 2, 3

Marco Buratti has conjectured that, given an odd prime p and a multiset L containing p ư 1 integers taken from {1, . ,pư1/2 }, there exists a Hamiltonian path in the complete graph with p vertices whose multiset of edgelengths is equal to L modulo p. We give a positive answer to this conjecture in the case of multisets of the type {1a, 2b , 3c } by completely classifying such multisets that are linearly or cyclically realizable.