Ranking tournaments with no errors II: Minimax relation

A tournament T=(V,A) is called cycle Mengerian (CM) if it satisfies the minimax relation on packing and covering cycles, for every nonnegative integral weight function defined on A. The purpose of this series of two papers is to show that a tournament is CM iff it contains none of four Möbius ladder...

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Bibliographic Details
Published inJournal of combinatorial theory. Series B Vol. 142; pp. 244 - 275
Main Authors Chen, Xujin, Ding, Guoli, Zang, Wenan, Zhao, Qiulan
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2020
Subjects
Algorithm
Duality
Feedback arc set
Integrality
Tournament
Integrality
Duality
Feedback arc set
Tournament
Algorithm
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Summary:A tournament T=(V,A) is called cycle Mengerian (CM) if it satisfies the minimax relation on packing and covering cycles, for every nonnegative integral weight function defined on A. The purpose of this series of two papers is to show that a tournament is CM iff it contains none of four Möbius ladders as a subgraph; such a tournament is referred to as Möbius-free. In the first paper we have given a structural description of all Möbius-free tournaments, and have proved that every CM tournament is Möbius-free. In this second paper we establish the converse by using our structural theorems and linear programming approach.
ISSN:0095-8956
1096-0902
DOI:10.1016/j.jctb.2019.10.004