Score vectors of Kotzig tournaments
โ Scribed by Lin Yucai; Huang Guoxun; Li Jiongsheng
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 410 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We obtain the asymptotic number of labeled trounaments with a given score sequence in the case where each score is nร2+O(n 3ร4+= ) for sufficiently small =>0. Some consequences for the score sequences of random tournaments are also noted. The method used is integration in n complex dimensions.
## Abstract A tournament is an oriented complete graph, and one containing no directed cycles is called __transitive__. A tournament __T__=(__V, A__) is called __m__โ__partition transitive__ if there is a partition such that the subtournaments induced by each __X__~__i__~ are all transitive, an
Ao and Hanson, and Guiduli, Gya ร rfa ร s, Thomasse ร 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 ร ร ร 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
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 s