• Corpus ID: 227239220

Paths of given length in tournaments.

@article{Sah2020PathsOG,
  title={Paths of given length in tournaments.},
  author={Ashwin Sah and Mehtaab Sawhney and Yufei Zhao},
  journal={arXiv: Combinatorics},
  year={2020}
}
What is the maximum possible number of directed k-edge paths in an n-vertex tournament? We are interested in the regime of fixed k and large n. The expected number of directed k-edge paths in a uniform random n-vertex tournament is n(n− 1) · · · (n− k)/2k = (1+ o(1))n(n/2)k . In this short note we show that one cannot do better, thereby confirming an unpublished conjecture of Jacob Fox, Hao Huang, and Choongbum Lee. Theorem 1. Every n-vertex tournament has at most n(n/2)k directed k-edge paths. 

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Kombinatorische Untersuchungen über den gerichteten vollständigen Graphen
  • Mat. Fiz. Lapok
  • 1943