The linear 3-arboricity of Kn,n and Kn

Abstract

A linear k-forest is a forest whose components are paths of length at most k. The linear k-arboricity of a graph G, denoted by la(k) (G), is the least number of linear k-forests needed to decompose G. In this paper, we completely determine lak (G) when G is a balanced complete bipartite graph K-n,K-n or a complete graph K-n, and k = 3. (C) 2007 Elsevier B.V. All rights reserved.