| 多部竞赛图中包含某条弧的圈 |
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| 引用本文： | 孟巍,李胜家.多部竞赛图中包含某条弧的圈[J].数学的实践与认识,2011,41(8). |
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| 作者姓名： | 孟巍 李胜家 |
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| 作者单位： | 山西大学数学科学学院,山西太原,030006 |
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| 摘 要： | 多部竞赛图或n部竞赛图是指一个完全n部无向图的定向图.2007年Volkmann证明了每个强连通的n部竞赛图(n≥3)至少存在一条弧它包含在从3到n的每个长度的圈中.在此基础上给出了强连通n部竞赛图中存在一条弧它包含在从3到n+1的每个长度的圈中的一个充分条件,并举例说明该条件在某种意义上的最佳可能性.
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| 关 键 词： | 多部竞赛图 圈 弧 |
On Cycles through an Arc in Multipartite Tournaments |
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| MENG Wei,LI Sheng-jia.On Cycles through an Arc in Multipartite Tournaments[J].Mathematics in Practice and Theory,2011,41(8). |
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| Authors: | MENG Wei LI Sheng-jia |
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| Affiliation: | MENG Wei,LI Sheng-jia (School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China) |
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| Abstract: | A multipartite or n-partite tournament is an orientation of a complete n-partite graph.In 2007,Volkmann proved that every strong n-partite tournament with n≥3 contains at least one arc that belongs to an m-cycle for each m∈{3,4,…,n}.In this paper we give a sufficient condition for strong n-partite tournaments such that there exists at least one arc which belongs to an m-cycle for every m∈{3,4,…,n +1}.By some examples we illustrate that this condition is in some sense best possible. |
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| Keywords: | multipartite tournaments cycles arcs |
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