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A Characterization of Unique Tournaments

✍ Scribed by Prasad Tetali

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
256 KB
Volume
72
Category
Article
ISSN
0095-8956

No coin nor oath required. For personal study only.

✦ Synopsis

We call a tournament unique, if there is no other tournament (barring isomorphic ones) which shares the same score vector. In this note, we provide a simple characterization of such unique tournaments.

1998 Academic Press

Theorem 1. There are exactly four (basic) strong tournaments in Unique (see Fig. 1); any other (nonstrong) tournament in Unique can be decomposed into strong components, each of which is one of the four basic tournaments.

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