The Linear Arboricity of Planar Graphs without 5-Cycles with two Chords

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