The linear (n-1)-arboricity of Cartesian product graphs

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 la(k)(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 C-nt(m) and K-n rectangle K-n,K-n,n are obtained.