Linear k-arboricity of complete bipartite graphs

摘要

A linear k-forest refers to a forest in which every component is a path of length at most k. The linear k-arboricity of a graph G is defined as the least number of linear k-forests, whose union is the set of all edges of G. Recently, Zuo et al. obtained the exact values of the linear 2- and 4-arboricity of complete bipartite graphs K-m,K-n for some m and n. In this paper, the exact values of the linear 2i-arboricity of complete bipartite graphs K-2in+2n,K-2in, K-2in+2n,K-2in+1 and K-2in+2n+1,K-2in are obtained, which can be seen as an extension of Zuo et al.' s results.