Buratti’s Conjecture on cyclic realizations

Prove that for every prime integer v, every multiset L of size v−1 with support contained in {1,2,…,⌊v/2⌋} has a cyclic realization.

Background

Buratti’s Conjecture concerns cyclic realizations of multisets of edge-lengths in complete graphs of prime order. A cyclic realization is a Hamiltonian path whose edge-lengths are measured using distance modulo v. The conjecture asserts universal realizability for multisets of the required size whose support consists only of admissible cyclic lengths.

The paper places this conjecture within a hierarchy of three realization conjectures and notes that the conjectures are known for supports of size at most two, while the paper focuses on multisets with support of size three.