Pancyclic out-arcs of a vertex in a hypertournament
Yubao Guo, Michel Surmacs · RWTH Publications (RWTH Aachen) · 2015
A k-hypertournament H on n vertices, where 2 ≤ k ≤ n ,i s ap air 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 S ⊆ V of order k, AH contains exactly one permutation of S as an arc. Inspired by the successful extension of classical results for tournaments (i.e. 2-hypertournaments) to hypertournaments, by Gutin and Yeo [J. Graph Theory 25 (1997), 277–286] and Li et al. [Discrete Appl. Math. 161 (2013), 2749–2752], we will prove the following: every strong k-hypertournament on n vertices, where n ≥ k +2 ≥ 3, contains a vertex all of whose out-arcs are pancyclic. This is a generalization of a known result for tournaments, by Yao et al. [Discrete Appl. Math. 99 (2000), 245–249]. Furthermore, our result is best possible in the sense that the bound n ≥ k + 2 is tight.