The Tournament Theorem of Rédei revisited
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912910948696064 |
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| author | Schweser, Thomas Stiebitz, Michael Toft, Bjarne |
| author_facet | Schweser, Thomas Stiebitz, Michael Toft, Bjarne |
| contents | In 1934 L. Rédei published his famous theorem that the number of Hamiltonian paths in a tournament is odd. In fact it is a corollary of a stronger theorem in his paper. Stronger theorems were also obtained in the early 1970s by G.A. Dirac in his lectures at Aarhus University and by C. Berge in his monographs on graphs and hypergraphs. We exhibit the stronger theorems of Rédei, Dirac and Berge and explain connections between them. The stronger theorem of Dirac has two corollaries, one equivalent to Rédei's stronger theorem and the other related to Berge's stronger theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Tournament Theorem of Rédei revisited Schweser, Thomas Stiebitz, Michael Toft, Bjarne Combinatorics 05C20 In 1934 L. Rédei published his famous theorem that the number of Hamiltonian paths in a tournament is odd. In fact it is a corollary of a stronger theorem in his paper. Stronger theorems were also obtained in the early 1970s by G.A. Dirac in his lectures at Aarhus University and by C. Berge in his monographs on graphs and hypergraphs. We exhibit the stronger theorems of Rédei, Dirac and Berge and explain connections between them. The stronger theorem of Dirac has two corollaries, one equivalent to Rédei's stronger theorem and the other related to Berge's stronger theorem. |
| title | The Tournament Theorem of Rédei revisited |
| topic | Combinatorics 05C20 |
| url | https://arxiv.org/abs/2510.10659 |