Ranking tournaments with no errors I: Structural description

doi:10.1016/j.jctb.2019.08.004

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	Ranking tournaments with no errors I: Structural description
	Chen, Xujin 2,3; Ding, Guoli 1; Zang, Wenan 4; Zhao, Qiulan 5
刊名	JOURNAL OF COMBINATORIAL THEORY SERIES B
	2020-03-01
卷号	141 页码:264-294
关键词	Tournament Feedback arc set Cycle packing Minimax relation Characterization
ISSN号	0095-8956
DOI	10.1016/j.jctb.2019.08.004
英文摘要	In this series of two papers we examine the classical problem of ranking a set of players on the basis of a set of pairwise comparisons arising from a sports tournament, with the objective of minimizing the total number of upsets, where an upset occurs if a higher ranked player was actually defeated by a lower ranked player. This problem can be rephrased as the so-called minimum feedback arc set problem on tournaments, which arises in a rich variety of applications and has been a subject of extensive research. In this series we study this NP-hard problem using structure-driven and linear programming approaches. Let T = (V, A) be a tournament with a nonnegative integral weight w(e) on each arc e. A subset F of arcs is called a feedback arc set if T\F contains no cycles (directed). A collection C of cycles (with repetition allowed) is called a cycle packing if each arc e is used at most w(e) times by members of C. We call T cycle Mengerian (CM) if, for every nonnegative integral function w defined on A, the minimum total weight of a feedback arc set is equal to the maximum size of a cycle packing. The purpose of these two papers is to show that a tournament is CM iff it contains none of four Mobius ladders as a subgraph; such a tournament is referred to as Mobius-free. In this first paper we present a structural description of all Mobius-free tournaments, which relies heavily on a chain theorem concerning internally 2-strong tournaments. (C) 2019 Elsevier Inc. All rights reserved.
资助项目	NSF of China[11801266] ; NSF of China[11531014] ; NSF[DMS-1500699] ; Research Grants Council of Hong Kong
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000508288900012
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50603]
专题	应用数学研究所
通讯作者	Zhao, Qiulan
作者单位	1.Louisiana State Univ, Math Dept, Baton Rouge, LA 70803 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Univ Hong Kong, Dept Math, Hong Kong, Peoples R China 5.Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China
推荐引用方式 GB/T 7714	Chen, Xujin,Ding, Guoli,Zang, Wenan,et al. Ranking tournaments with no errors I: Structural description[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B,2020,141:264-294.
APA	Chen, Xujin,Ding, Guoli,Zang, Wenan,&Zhao, Qiulan.(2020).Ranking tournaments with no errors I: Structural description.JOURNAL OF COMBINATORIAL THEORY SERIES B,141,264-294.
MLA	Chen, Xujin,et al."Ranking tournaments with no errors I: Structural description".JOURNAL OF COMBINATORIAL THEORY SERIES B 141(2020):264-294.