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On Score Sequences ofk-Hypertournaments

Authors
Journal
European Journal of Combinatorics
0195-6698
Publisher
Elsevier
Publication Date
Volume
21
Issue
8
Identifiers
DOI: 10.1006/eujc.2000.0393
Disciplines
  • Mathematics

Abstract

Abstract Given two nonnegative integers n and k with n ≥ k > 1, a k -hypertournament on n vertices is a pair ( V, A), where V is a set of vertices with | V | = n and A is a set of k -tuples of vertices, called arcs, such that for any k -subset S of V , A contains exactly one of the k!k -tuples whose entries belong to S. We show that a nondecreasing sequence ( r 1, r 2,⋯ , r n ) of nonnegative integers is a losing score sequence of a k -hypertournament if and only if for each j(1 ≤ j ≤ n),with equality holding when j = n. We also show that a nondecreasing sequence ( s 1, s 2 ,⋯ , s n ) of nonnegative integers is a score sequence of some k -hypertournament if and only if for each j(1 ≤ j ≤ n),with equality holding when j = n. Furthermore, we obtain a necessary and sufficient condition for a score sequence of a strong k -hypertournament. The above results generalize the corresponding theorems on tournaments.

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