Graphs and Combinatorics

, Volume 36, Issue 1, pp 139–151 | Cite as

The Number of Tournaments with the Minimum Number of Upsets

  • Ilhan HaciogluEmail author
  • Nuri Sendil
  • Burak Kurkcu
  • Carlos M. da Fonseca
Original Paper


In this paper we provide a construction method which generates all tournament matrices with a prescribed score-list with minimum number of upsets. We set up a correspondence between a tournament matrix with minimum number of upsets and perfect matchings. We provide some upper bounds for the tournament matrices with minimum number of upsets by using bounds for the permanents of Ferrers matrices. Several examples and related problems are also discussed.


Tournaments Upsets 

Mathematics Subject Classification

05C20 05C85 



We thank the referees for all the valuable comments which helped the presentation of this paper.


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Copyright information

© Springer Japan KK, part of Springer Nature 2020

Authors and Affiliations

  • Ilhan Hacioglu
    • 1
    Email author
  • Nuri Sendil
    • 1
  • Burak Kurkcu
    • 2
  • Carlos M. da Fonseca
    • 3
  1. 1.College of Engineering and TechnologyAmerican University of the Middle EastKuwait CityKuwait
  2. 2.IstanbulTurkey
  3. 3.University of Primorska, FAMNITKoperSlovenia

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