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PreprintCC0arXiv

Alternating Hamilton Paths and Cycles in Poset Products

  • Yuxian Dong
  • Jianxi Mao
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Abstract

We study alternating Hamilton paths and cycles in the comparability graphs of finite posets. We prove that if a finite poset P with at least two elements admits an alternating Hamilton path, then P× Br admits an alternating Hamilton cycle for every r≥2, where Br is the Boolean lattice. As a corollary, we settle a conjecture of Katona [Discrete Appl. Math., 2013]. Furthermore, we characterize the divisor lattices admitting alternating Hamilton paths and cycles.

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Cite

BibTeXRIS
BibTeX
@misc{dong2026alternating,
  title = {{Alternating Hamilton Paths and Cycles in Poset Products}},
  author = {Yuxian Dong and Jianxi Mao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18152},
  eprint = {2610.18152},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18152},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Alternating Hamilton Paths and Cycles in Poset Products
AU  - Yuxian Dong
AU  - Jianxi Mao
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18152
UR  - https://arxiv.org/abs/2610.18152
AB  - We study alternating Hamilton paths and cycles in the comparability graphs of finite posets. We prove that if a finite poset P with at least two elements admits an alternating Hamilton path, then P× B_r admits an alternating Hamilton cycle for every r≥2, where B_r is the Boolean lattice. As a corollary, we settle a conjecture of Katona [Discrete Appl. Math., 2013]. Furthermore, we characterize the divisor lattices admitting alternating Hamilton paths and cycles.
ER  -