Hamiltonicity and cycle factors in k-quasi-transitive digraphs of large diameter

@misc{zhang2026hamiltonicity,
  title = {{Hamiltonicity and cycle factors in k-quasi-transitive digraphs of large diameter}},
  author = {Hao Zhang and Panpan Cheng},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06310},
  eprint = {2611.06310},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06310},
}

TY  - UNPB
TI  - Hamiltonicity and cycle factors in k-quasi-transitive digraphs of large diameter
AU  - Hao Zhang
AU  - Panpan Cheng
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06310
UR  - https://arxiv.org/abs/2611.06310
AB  - A digraph is k-quasi-transitive if the endpoints of every directed path of length k are adjacent. In this paper, we prove that every strong non-bipartite k-quasi-transitive digraph of diameter at least k+2 is Hamiltonian when k≥7 is odd. Moreover, combined with the known even case, for k≥6, we also prove that a strong bipartite k-quasi-transitive digraph of diameter at least k+2 is Hamiltonian if and only if it has a cycle factor. These answer two problems posed by Alva-Samos and Hernández-Cruz affirmatively [Journal of Graph Theory \textbf{96} (2021) 310--325].
ER  -