2026/07/28 by Mohammed Lalou, Nader Mbarek, Abdallah Skender +1 · 1 citation
Mathematics · #math.CO
In this paper, we prove the existence of two completely independent spanning trees in the n-dimensional dual-cube Fn, a variant of the hypercube, for every n ≥ 5. To this end, we use the hypercube structure of the clusters of Fn to extend the construction of CIST from the (n-1)-dimensional hypercube to the dual-cube. In addition, we propose a recursive algorithm that builds the two trees while improving their diameters. Finally, we propose a conjecture concerning the existence of k completely independent spanning trees in the dual-cube.