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正则多部竞赛图的竞争指数

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正则多部竞赛图的竞争指数 张新鸿1, 郭燕1, 李瑞娟2, 张越11 太原科技大学应用科学学院, 太原 030024;
2 山西大学数学科学学院, 太原 030006 The Competition Index of Regular Multipartite Tournaments ZHANG Xinhong1, GUO Yan1, LI Ruijuan2, ZHANG Yue11 School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China;
2 School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
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摘要D是一个有向图,若存在无向图G满足:(1)G的顶点集与D的顶点集相同;(2)任取D中的两个顶点x,y,其在G中相邻当且仅当存在D中顶点z,使得D中包含一条从xz的长为m的有向途径和一条从yz的长为m的有向途径,则称GDm步竞争图,记为G=CmD).2004年,Cho和Kim首次提出竞争指数的概念.若对于某个正整数r和所有非负整数i,存在最小正整数q,使得Cq+iD)=Cq+i+rD),则称整数qD的竞争指数,记为cindex (D).2008年,Kim给出了竞赛图的竞争指数的上界.2009年,Akelbek和Kirkland给出了本原有向图的竞争指数.文中研究并计算了正则多部竞赛图的竞争指数.
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收稿日期: 2006-01-09
PACS:05C20
05C75
05C90
基金资助:山西省应用基础研究项目(201801D121013),山西省优秀青年基金项目(201901D211197).

引用本文:
张新鸿, 郭燕, 李瑞娟, 张越. 正则多部竞赛图的竞争指数[J]. 应用数学学报, 2021, 44(3): 330-339. ZHANG Xinhong, GUO Yan, LI Ruijuan, ZHANG Yue. The Competition Index of Regular Multipartite Tournaments. Acta Mathematicae Applicatae Sinica, 2021, 44(3): 330-339.
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[11] 李瑞娟, 刘东婷. 正则多部竞赛图的控制图. 应用数学学报, 2016, 39(4): 555-561(Li Ruijuan, Liu Dongting. The Domination Graph of a Regular Multipartite Tournament. Acta Mathematicae Applicatae Sinica, 2016, 39(4): 555–561)

[1]李瑞娟, 刘冬婷. 正则多部竞赛图的控制图[J]. 应用数学学报, 2016, 39(4): 555-561.
[2]崔丽楠, 郭巧萍. 几乎正则多部竞赛图中弧的外路[J]. 应用数学学报, 2016, 39(1): 130-137.



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