The Linear Arboricity of Planar Graphs Without 5-Cycles With Two Chords

Xiang-Lian Chen, Jian-Liang Wu

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 $G$, $la(G)=\lceil(\Delta(G)/2)\rceil$ if $\Delta(G)\geq7$ and $G$ has no 5-cycles with two chords.