ON TOURNAMENTS OF SMALL ORDERS AND THEIR APPLICATIONS

Guo Fei ZHOU;Ke Min ZHANG

系统科学与复杂性(英文) ›› 2003, Vol. 16 ›› Issue (4) : 475-482.

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系统科学与复杂性(英文) ›› 2003, Vol. 16 ›› Issue (4) : 475-482.
论文

ON TOURNAMENTS OF SMALL ORDERS AND THEIR APPLICATIONS

    Guo Fei ZHOU(1),Ke Min ZHANG(2)
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ON TOURNAMENTS OF SMALL ORDERS AND THEIR APPLICATIONS

    Guo Fei ZHOU(1),Ke Min ZHANG(2)
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摘要

In this paper, we generate all nonisomorphic tournaments of order at most nine, all nonisomorphic almost regular tournaments of order 10 and all nonisomorphic regular tournaments of order 11. For each of these tournaments, we have given its score-list, connectivity, diameter, the minimal number of feedbacks, automorphisms and spectra. Moreover, we have verified the well-known Kelly's Conjecture for n = 2k + 1 < 11. And we also determine the n-universal tournaments for n < 6. However, several related results are given and some related open problems are raised.

Abstract

In this paper, we generate all nonisomorphic tournaments of order at most nine, all nonisomorphic almost regular tournaments of order 10 and all nonisomorphic regular tournaments of order 11. For each of these tournaments, we have given its score-list, connectivity, diameter, the minimal number of feedbacks, automorphisms and spectra. Moreover, we have verified the well-known Kelly's Conjecture for n = 2k + 1 < 11. And we also determine the n-universal tournaments for n < 6. However, several related results are given and some related open problems are raised.

关键词

Tournaments / applications

Key words

Tournaments / applications

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Guo Fei ZHOU , Ke Min ZHANG. ON TOURNAMENTS OF SMALL ORDERS AND THEIR APPLICATIONS. 系统科学与复杂性(英文), 2003, 16(4): 475-482
Guo Fei ZHOU , Ke Min ZHANG. ON TOURNAMENTS OF SMALL ORDERS AND THEIR APPLICATIONS. Journal of Systems Science and Complexity, 2003, 16(4): 475-482
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