The linear (n-1)-arboricity of Cartesian product graphs
Liancui Zuo, Shengjie He, Bing Xue · Applicable Analysis and Discrete Mathematics · 2015
A linear k-forest of an undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity of G, denoted by lak(G), is the minimum number of linear k-forests needed to partition the edge set E(G) of G. In this paper, the exact values of the linear (n-1)-arboricity of Hamming graph, and Cartesian product graphs Cm nt and Kn_Kn,n are obtained.