Table of Contents
International Journal of Combinatorics
Volume 2013, Article ID 501701, 6 pages
http://dx.doi.org/10.1155/2013/501701
Research Article

The Linear 2- and 4-Arboricity of Complete Bipartite Graph

1College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
2School of Mathematics, Shandong University, Jinan 250100, China

Received 7 August 2013; Accepted 30 October 2013

Academic Editor: Jun-Ming Xu

Copyright © 2013 Liancui Zuo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A linear -forest of an undirected graph is a subgraph of whose components are paths with lengths at most . The linear -arboricity of , denoted by ( ), is the minimum number of linear -forests needed to decompose . In case the lengths of paths are not restricted, we then have the linear arboricity of , denoted by ( ). In this paper, the exact value of the linear 2- and 4-arboricity of complete bipartite graph for some and is obtained.