在对偶立方体中构建两棵完全独立的生成树
Constructing two completely independent spanning trees in dual-cubes
- Université Bourgogne Europe（勃艮第欧洲大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究在\(n\geq5\)的\(n\)维对偶立方体\(F_n\)中构建两棵完全独立生成树的问题，利用\(F_n\)簇超立方体结构扩展构造方法，并提出递归算法减小树直径，还对\(k\)棵树的存在性提出猜想。
AI中文摘要：
本文证明了对于每个\(n\geq5\)，在\(n\)维对偶立方体\(F_n\)（超立方体的一种变体）中存在两棵完全独立的生成树。为此，利用\(F_n\)簇的超立方体结构将完全独立生成树（CIST）的构造从\((n - 1)\)维超立方体扩展到对偶立方体。还提出一种递归算法来构建这两棵树并减小其直径。最后，提出了关于对偶立方体中\(k\)棵完全独立生成树存在性的猜想。
英文摘要：
In this paper, we prove the existence of two completely independent spanning trees in the $n$-dimensional dual-cube $F_n$, a variant of the hypercube, for every $n \geq 5$. To this end, we use the hypercube structure of the clusters of $F_n$ to extend the construction of CIST from the $(n-1)$-dimensional hypercube to the dual-cube. In addition, we provide a recursive algorithm that builds the two trees while improving their diameters. Finally, we propose a conjecture regarding the existence of $k$ completely independent spanning trees in the dual-cube.
