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arXiv · 2610.18152

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 $P\times B_r$ admits an alternating Hamilton cycle for every $r\ge2$, 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.

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Yuxian Dong, Jianxi Mao. 2026-10-13. Alternating Hamilton Paths and Cycles in Poset Products. https://arxiv.org/abs/2610.18152

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