## Abstract A finite tournament __T__ is __tight__ if the class of finite tournaments omitting __T__ is wellβquasiβordered. We show here that a certain tournament __N__~5~ on five vertices is tight. This is one of the main steps in an exact classification of the tight tournaments, as explained in [
Logrolling and a McGarvey theorem for separable tournaments
β Scribed by Guillaume Hollard; Michel Breton
- Publisher
- Springer
- Year
- 1996
- Tongue
- English
- Weight
- 265 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0176-1714
No coin nor oath required. For personal study only.
β¦ Synopsis
In this note we prove a McGarvey theorem for the family of Separable Tournaments. This family arises in the analysis of Logrolling and Vote Trading in Committees.
The authors would like to thank N.R. Miller for sending us Miller (1994), E. Hopkins and F. Mouton for useful comments on early versions of the manuscript, and two anonymous referees for detailed reports.
π SIMILAR VOLUMES
Let E denote the group of units (i.e., the reduce set of residues) in the ring Z3p,,n. Here we consider q,p to be primes, q = 3 (mod 4), q 2 7, p = 1 (mod 4). Let W denote a common primitive root of 3, q, and p 2 . If H denotes the (normal) subgroup of E that is generated by {-1, W } , we show that
Ao and Hanson, and Guiduli, Gya Γ rfa Γ s, Thomasse Γ and Weidl independently, proved the following result: For any tournament score sequence S (s 1 , s 2 ,F F F,s n ) with s 1 s 2 Γ Γ Γ s n , there exists a tournament T on vertex set f1Y 2Y F F F Y ng such that the score of each vertex i is s i an