Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Dong, Yuxian, Mao, Jianxi
Institution: Dalian University of Technology
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221809018