Volume 36 • Number 2 • 2013   • The Linear Arboricity of Planar Graphs without 5-Cycles with Chords Hong-Yu Chen, Xiang Tan and Jian-Liang Wu Abstract. The linear arboricity $la(G)$ of a graph $G$ is the minimum number of linear forests which partition the edges of $G$. In this paper, it is proved that for a planar graph $G$ with maximum degree $\Delta(G)\geq7$, $la(G)=\lceil\frac{\Delta(G)}{2}\rceil$ if $G$ has no 5-cycles with chords. 2010 Mathematics Subject Classification: 05C15 Full text: PDF