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A k-hypertournament H on n vertices, where 2 ≤ k ≤ 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 ⊆ 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 ≤ k ≤ 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 ≤ k ≤ n−2, and C is a Hamiltonian cycle in H, then C contains at least three pancyclic arcs.
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참고문헌 (11)
참고문헌 신청
A. Yeo / 2005 / The number of pancyclic arcs in a k-strong tournament / J. Graph Theory 50 (3) : 212 ~ 219
G. Gutin / 1997 / Hamiltonian paths and cycles in hypertournaments / J. Graph Theory 25 (4) : 277 ~ 286
H. Li / 2013 / On the vertex-pancyclicity of hypertournaments / Discrete Appl. Math 161 (16-17) : 2749 ~ 2752
J. W. Moon / 1966 / On subtournaments of a tournament / Canad. Math. Bull 9 : 297 ~ 301
J. W. Moon / 1994 / On k-cyclic and pancyclic arcs in strong tournaments / J. Combin. Inform. System Sci 19 (3-4) : 207 ~ 214
G. Gutin / 1997 / Hamiltonian paths and cycles in hypertournaments / J. Graph Theory 25 (4) : 277 ~ 286
H. Li / 2013 / On the vertex-pancyclicity of hypertournaments / Discrete Appl. Math 161 (16-17) : 2749 ~ 2752
J. W. Moon / 1966 / On subtournaments of a tournament / Canad. Math. Bull 9 : 297 ~ 301
J. W. Moon / 1994 / On k-cyclic and pancyclic arcs in strong tournaments / J. Combin. Inform. System Sci 19 (3-4) : 207 ~ 214
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