@article{Hong2023, 
author = {Xia Hong and Wei Feng},
title = {Completely independent spanning trees in some Cartesian product graphs},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {16127-16136},
keywords = {completely independent spanning tree, Cartesian product graph, path, cycle, wheel, complete bipartite graph, complete tripartite graph},
url = {https://www.sciopen.com/article/10.3934/math.2023823},
doi = {10.3934/math.2023823},
abstract = {Let        T          1        ,      T          2        ,  …  ,      T          k       be spanning trees of a graph    G. For any two vertices    u  ,  v of    G, if the paths from    u to    v in these    k trees are pairwise openly disjoint, then we say that        T          1        ,      T          2        ,  …  ,      T          k       are completely independent. Hasunuma showed that there are two completely independent spanning trees in any 4-connected maximal planar graph, and that given a graph    G, the problem of deciding whether there exist two completely independent spanning trees in    G is NP-complete. In this paper, we consider the number of completely independent spanning trees in some Cartesian product graphs such as        W          m        ◻      P          n        ,        W          m        ◻      C          n        ,        K          m      ,      n        ◻      P          r        ,        K          m      ,      n        ◻      C          r        ,        K          m      ,      n      ,      r        ◻      P          s        ,        K          m      ,      n      ,      r        ◻      C          s      .}
}