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arXiv · 2608.15287

Hamiltonian paths in the permutation digraphs $P(n,n-2)$

Jiaxin Guo·Ming Duan·Jie Xue
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Abstract

For $1\leq k<n$, let $P(n,k)$ be the directed overlap graph whose vertices are the $k$-permutations of $[n]$ and whose arcs are the $(k+1)$-permutations. Isaak proved that $P(n,n-2)$ has no directed Hamiltonian cycle for $n\geq4$ and asked whether it nevertheless has a directed Hamiltonian path. We answer this question affirmatively by showing that $P(n,n-2)$ has a Hamiltonian path.

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Jiaxin Guo, Ming Duan, Jie Xue. 2026-08-15. Hamiltonian paths in the permutation digraphs $P(n,n-2)$. https://arxiv.org/abs/2608.15287

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