A k-hypertournament H on n vertices, where 2≤k≤n, is a pair H=(V,A_H), where V is the vertex set of H and A_H is a set of k-tuples of vertices, called arcs, such that, for all subsets S?V with |S|=k, A_H contains exactly one permutation of S as an arc. Gutin and Yeo (1997) showed in [2] that any strong k-hypertournament H on n vertices, where 3≤k≤n-2, is Hamiltonian, and posed the question as to whether the result could be extended to vertex-pancyclicity. As a response, Petrovic and Thomassen (2006) in [4] and Yang (2009) in [6] gave some sufficient conditions for a strong hypertournament to be vertex-pancyclic. In this paper, we prove that, if H is a strong k-hypertournament on n vertices, where 3≤k≤n-2, then H is vertex-pancyclic. This extends the aforementioned results and Moon's theorem for tournaments. Furthermore, our result is best possible in the sense that the bound k≤n-2 is tight.
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机译：n个顶点上的k个超级锦标赛H，其中2≤k≤n是对H =（V，A_H），其中V是H的顶点集，而A_H是一组k个顶点的元组，称为圆弧，这样，对于| S | = k的所有子集S？V，A_H恰好包含S的一个置换作为弧。 Gutin和Yeo（1997）在[2]中指出，n个顶点上的任何强k-超曲线H（3≤k≤n-2）是哈密顿量，并提出了一个问题，即结果是否可以扩展到顶点-泛环性。作为回应，Petrovic和Thomassen（2006）在[4]中和Yang（2009）在[6]中给出了使强超锦标赛成为顶点泛环的一些充分条件。在本文中，我们证明，如果H是n个顶点上的强k-超锦标赛，其中3≤k≤n-2，则H是顶点-泛环。这扩展了上述结果和锦标赛的Moon定理。此外，在约束k≤n-2严格的意义上说，我们的结果是最好的。
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