Transitive oriented 3-Hypergraphs of cyclic orders
  In this paper we introduce the definition of transitivity for oriented 3-hypergraphs in order to study partial and complete cyclic orders. This definition allow us to give sufficient conditions on a partial cyclic order to be totally extendable. Furthermore, we introduce the 3-hypergraph associated to a cyclic permutation and characterize it in terms of cyclic comparability 3-hypergraphs. 
Natalia Garcia-Colin, Amanda Montejano, Luis Montejano, Deborah   Oliveros
math.CO