English

Oriented Hamiltonian Cycles in Tournaments: a Proof of Rosenfeld's Conjecture

Combinatorics 2023-02-10 v2

Abstract

Rosenfeld in 1974 conjectured that there is an integer N > 8 such that every tournament of order n > N contains every non-directed cycle of order n. We prove that, with exactly 35 exceptions, every tournament of order n > 2 contains each non-directed cycle of order m, 2 < m < n+1.

Keywords

Cite

@article{arxiv.2204.11211,
  title  = {Oriented Hamiltonian Cycles in Tournaments: a Proof of Rosenfeld's Conjecture},
  author = {Ayman El Zein},
  journal= {arXiv preprint arXiv:2204.11211},
  year   = {2023}
}