Linear 3-Arboricity of the Balanced Complete

Abstract

A linear $k$-forest is a graph whose components are paths with lengths at most $k$. The minimum number of linear $k$-forests needed to decompose a graph $G$ is the linear $k$-arboricity of $G$ and is denoted by $l{a}_k(G)$. In this paper, we study the linear $3$-arboricity of balanced complete multipartite graphs and we obtain some substantial results.