✦ LIBER ✦

Asymptotic enumeration of tournaments with a given score sequence containing a specified digraph

✍ Scribed by Zhicheng Gao; Brendan D. McKay; Xiaoji Wang

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 122 KB
Volume: 16
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(200001)16:1<47::aid-rsa4>3.0.co;2-l

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✦ Synopsis

This paper studies the probability that a random tournament with specified score sequence contains a specified subgraph. The exact asymptotic value is found in the case that the scores are not too far from regular and the subgraph is not too large. An ndimensional saddle-point method is used. As a sample application, we prove that almost all tournaments with a given score sequence (not too far from regular) have a trivial automorphism group.