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PANCYCLIC ARCS IN HAMILTONIAN CYCLES OF HYPERTOURNAMENTS

  • Guo, Yubao (Lehrstuhl C fur Mathematik RWTH Aachen University) ;
  • Surmacs, Michel (Lehrstuhl C fur Mathematik RWTH Aachen University)
  • Received : 2013.09.09
  • Published : 2014.11.01

Abstract

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.

Keywords

References

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Cited by

  1. Regular Hypertournaments and Arc-Pancyclicity vol.84, pp.2, 2017, https://doi.org/10.1002/jgt.22019
  2. On pancyclic arcs in hypertournaments vol.215, 2016, https://doi.org/10.1016/j.dam.2016.07.017