Regular Hypertournaments and Arc‐Pancyclicity
Michel Surmacs · Journal of Graph Theory · 2016
Abstract Ak‐hypertournamentHonnvertices ( ) is a pair , whereVis the vertex set ofHandAis a set ofk‐tuples of vertices, called arcs, such that for all subsets with ,Acontains exactly one permutation ofSas an arc. Recently, Li et al. showed that any strongk‐hypertournamentHonnvertices, where , is vertex‐pancyclic, an extension of Moon's theorem for tournaments. In this article, we examine several generalizations of regular tournaments and prove the following generalization of Alspach's theorem concerning arc‐pancyclicity: Every Σ‐regulark‐hypertournament onnvertices, where , is arc‐pancyclic.