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 m nt and Kn Kn,n are obtained