Triangle-different Hamiltonian paths

Let G be a fixed graph. Two paths of length n−1 on n vertices (Hamiltonian paths) are G-different if there is a subgraph isomorphic to G in their union. In this paper we prove that the maximal number of pairwise triangle-different Hamiltonian paths is equal to the number of balanced bipartitions of the ground set, answering a question of Körner, Messuti and Simonyi.