Linear A;-arboricity of complete bipartite graphs

Abstract

A linear c-forest refers to a forest in which every component is a path of length at most k. The linear fc-arboricity of a graph G is defined as the least number of linear fc-forests, whose union is the set of all edges of G. Recently, Zuo et al. obtained the exact values of the linear 2- A nd 4-arboricity of complete bipartite graphs Km, for some m and n. In this paper, the exact values of the linear 2i- A rboricity of complete bipartite graphs i2n+2n,2>n, i2n+2n,2n+i and K2in+2n+i,2in are obtained, which can be seen as an extension of Zuo et al.1 s results. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.