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On the vertex-pancyclicity of hypertournaments

https://doi.org/10.1016/j.dam.2013.05.036Get rights and content
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Abstract

A k-hypertournament H on n vertices, where 2kn, is a pair H=(V,AH), where V is the vertex set of H and AH is a set of k-tuples of vertices, called arcs, such that, for all subsets SV with |S|=k, AH 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 3kn2, 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 3kn2, 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 kn2 is tight.

Keywords

Tournament
Hypertournament
Vertex-pancyclicity

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