Linear K-arboricity of complete bipartite graphs

Abstract

A linear K-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,n for some m and n. In this paper, the exact values of the linear 2i- A xboricity of complete bipartite graphs Kun+in.iin, K2in+2n,2in+i and i2in+2n+i,2n are obtained, which can be seen as an extension of Zuo et al.' s results. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.