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 (FAS) if T\F contains no cycles (directed). A collection F of FASs (with repetition allowed) is called an FAS packing if each arc e is used at most w(e) times by the members of F. The purpose of this paper is to give a characterization of all tournaments T=(V,A) with the property that, for every nonnegative integral weight function w defined on A, the minimum total weight of a cycle is equal to the maximum size of an FAS packing. 

　　Publication: 

　　Mathematics of Operations Research, Published Online: 23 Feb, 2023, https://doi.org/10.1287/moor.2023.1352 

　　Author: 

　　Xujin Chen 

　　Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　Email: xchen@amss.ac.cn 

　　Guoli Ding 

　　Mathematics Department, Louisiana State University, Baton Rouge, LA 70803, USA 

　　Wenan Zang 

　　Department of Mathematics, The University of Hong Kong, Hong Kong, China 

　　Qiulan Zhao 

　　Department of Mathematics, Nanjing University, Nanjing 210093, China