• The Pure and Applied Mathematics
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• v.8 no.2
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• pp.185-191
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• 2001

A k-hypertournament is a complete k-hypergraph with all k-edges endowed with orientations, i.e., orderings of the vertices in the edges. The incidence matrix associated with a k-hypertournament is called a 7-hypertournament matrix, where each row stands for a vertex of the hypertournament. Some properties of the hypertournament matrices are investigated. The sequences of the numbers of 1＇s and -1＇s of rows of a k-hypertournament matrix are respectively called the score sequence (resp. losing score sequence) of the matrix and so of the corresponding hypertournament. A necessary and sufficient condition for a sequence to be the score sequence (resp. the losing score sequence) of a k-hypertournament is proved.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1141-1154
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• 2014

A k-hypertournament H on n vertices, where $2{\leq}k{\leq}n$, is a pair H = (V,A), where V is the vertex set of H and A is a set of k-tuples of vertices, called arcs, such that for all subsets $S{\subseteq}V$ with |S| = k, A contains exactly one permutation of S as an arc. Recently, Li et al. showed that any strong k-hypertournament H on n vertices, where $3{\leq}k{\leq}n-2$, is vertex-pancyclic, an extension of Moon's theorem for tournaments. In this paper, we prove the following generalization of another of Moon's theorems: If H is a strong k-hypertournament on n vertices, where $3{\leq}k{\leq}n-2$, and C is a Hamiltonian cycle in H, then C contains at least three pancyclic arcs.