The Number of Tournaments with the Minimum Number of Upsets

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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.

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

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Correspondence to Ilhan Hacioglu.

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Dedicated to the memory of T.S. Michael.

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Hacioglu, I., Sendil, N., Kurkcu, B. et al. The Number of Tournaments with the Minimum Number of Upsets. Graphs and Combinatorics 36, 139–151 (2020).

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  • Tournaments
  • Upsets

Mathematics Subject Classification

  • 05C20
  • 05C85