The linear k-arboricity of Cartesian product of multipartite balanced complete graphs

A linear k-forest of an undirect graph G is a subgraph whose components are paths with length at most k. The linear k-arboricity of G, denoted by lak (G), is the min- imum number of linear k-forests partitioning the edge set E (G). In the present paper, we studied the linear (n-1)-arboricity of Cartesian product graph (Kn,n)[m] and (Kn(l) )[m], and obtained the exact values of linear (n - 1)-arboricity of (Kn,n)[m] and (Kn(l) )[m] in some special cases. © International Association of Engineers.