A Result on Linear Arboricity of Planar Graphs

Abstract

The linear arboricity $la(G)$ of a graph $G$ is the minimum number of linear forests that partition the edges of $G$. In this paper, it is proved that if $G$ is a planar graph with maximum degree $\mathrm{\Delta }\ge 7$ and every $7$-cycle of $G$ contains at most two chords, then $la(G)=\lceil \frac{\mathrm{\Delta }(G)}{2}\rceil$.