On Score Sequences ofk-Hypertournaments
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 belo...
Saved in:
Published in | European journal of combinatorics Vol. 21; no. 8; pp. 993 - 1000 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Ltd
01.11.2000
|
Online Access | Get full text |
Cover
Loading…
Summary: | 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. |
---|---|
ISSN: | 0195-6698 1095-9971 |
DOI: | 10.1006/eujc.2000.0393 |