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 \(\Delta \geq 7\) and every \(7\)-cycle of \(G\) contains at most two chords, then \(la(G) = \left\lceil \frac{\Delta(G)}{2} \right\rceil\).