PANCYCLIC ARCS IN HAMILTONIAN CYCLES OF HYPERTOURNAMENTS

Title & Authors
PANCYCLIC ARCS IN HAMILTONIAN CYCLES OF HYPERTOURNAMENTS
Guo, Yubao; Surmacs, Michel;

Abstract
A k-hypertournament H on n vertices, where $\small{2{\leq}k{\leq}n}$, 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 $\small{S{\subseteq}V}$ 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 $\small{3{\leq}k{\leq}n-2}$, 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 $\small{3{\leq}k{\leq}n-2}$, and C is a Hamiltonian cycle in H, then C contains at least three pancyclic arcs.
Keywords
tournament;hypertournament;semicomplete digraph;pancyclic arc;Hamiltonian cycle;
Language
English
Cited by
1.
On pancyclic arcs in hypertournaments, Discrete Applied Mathematics, 2016, 215, 164
2.
Regular Hypertournaments and Arc-Pancyclicity, Journal of Graph Theory, 2017, 84, 2, 176
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