On Score Sequences ofk-Hypertournaments

• Published in: European journal of combinatorics Vol. 21; no. 8; pp. 993 - 1000
• Main Authors: Guofei, Zhou, Tianxing, Yao, Kemin, Zhang
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2000
• ISSN: 0195-6698; 1095-9971
• DOI: 10.1006/eujc.2000.0393

Given two nonnegative integers n and k withn≥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 ofV , A contains exactly one of the k!k -tuples whose entries belong to S. We show that a nondecreasing sequence (r1, r2,⋯ , rn) 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 whenj=n. We also show that a nondecreasing sequence (s1,s2 ,⋯ , sn) of nonnegative integers is a score sequence of somek -hypertournament if and only if for each j(1 ≤j≤n),with equality holding whenj=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.