置换有向图$P(n,n-2)$中的哈密顿路径
Hamiltonian paths in the permutation digraphs $P(n,n-2)$
首次发表
浏览论文内容
中文总结 AI 辅助
该研究针对Isaak提出的问题，证明了$n\geq4$时无有向哈密顿环的置换有向图$P(n,n-2)$存在有向哈密顿路径，给出了肯定答案。
中文摘要 AI 辅助
对于$1\leq k<n$，令$P(n,k)$为有向重叠图，其顶点是$[n]$的$k$-排列，弧是$(k+1)$-排列。Isaak证明当$n\geq4$时$P(n,n-2)$无有向哈密顿环，并询问它是否仍有有向哈密顿路径。我们通过证明$P(n,n-2)$存在哈密顿路径，肯定回答了该问题。
英文摘要
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.
