| 最省和最奢的2—竞赛矩阵 |
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| 引用本文： | 侯耀平.最省和最奢的2—竞赛矩阵[J].应用数学学报,2001,24(4):533-538. |
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| 作者姓名： | 侯耀平 |
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| 作者单位： | 湖南师范大学数学系, |
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| 基金项目： | 国家自然科学基金(19971086号)资助项目. |
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| 摘 要： | 本文考虑以允许平局的单循环比赛为模型的2－竞赛图（二重完全图的定向图0和它的邻接矩阵（2－竞赛矩阵）。得到了得分向量与2－圈数，3－圈数之间的关系；给出了构造最省和最奢的2－竞赛矩阵的方法；部分地回答了文献4]中的一个问题。
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| 关 键 词： | 竞赛图 竞赛矩阵 得分向量 单循环比赛 组合数学 |
PARSIMONIOUS AND IMPROVIDENT 2-TOURNAMENT MATRICES |
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| HOU YAOPING.PARSIMONIOUS AND IMPROVIDENT 2-TOURNAMENT MATRICES[J].Acta Mathematicae Applicatae Sinica,2001,24(4):533-538. |
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| Authors: | HOU YAOPING |
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| Abstract: | In this paper we extend some concepts of tournaments to 2-tournaments, give conditions for an arbitrary nonegative integers vector to be score vector, obtain the relation among the number of 3-cycles, 2-cycles of a 2-tournament and its score vector a, and obtain the maximum and minimum number of 2-cycles with prescribed score vector s, partly answer a open problem of 4]. |
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| Keywords: | Tournament graph tournament matrix score vector maximum minimum |
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