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PreprintCC BY 4.0arXiv

Tournaments with many Hamilton cycles

  • N. C. Wormald
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Abstract

The object of interest is the maximum number, h(n), of Hamilton cycles in an n-tournament. By considering the expected number of Hamilton cycles in various classes of random tournaments, we obtain new asymptotic lower bounds on h(n). The best result so far is approximately $ 2.85584...$ times the expected number g(n) of Hamilton cycles in a random n-tournament, and it is conjectured that h(n)∼ cg(n) where c≈ 2.855958. The same statements hold for Hamilton paths.

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Cite

BibTeXRIS
BibTeX
@misc{wormald2026tournaments,
  title = {{Tournaments with many Hamilton cycles}},
  author = {N. C. Wormald},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16245},
  eprint = {2610.16245},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16245},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Tournaments with many Hamilton cycles
AU  - N. C. Wormald
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16245
UR  - https://arxiv.org/abs/2610.16245
AB  - The object of interest is the maximum number, h(n), of Hamilton cycles in an n-tournament. By considering the expected number of Hamilton cycles in various classes of random tournaments, we obtain new asymptotic lower bounds on h(n). The best result so far is approximately $ 2.85584...$ times the expected number g(n) of Hamilton cycles in a random n-tournament, and it is conjectured that h(n)∼ cg(n) where c≈ 2.855958. The same statements hold for Hamilton paths.
ER  -