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

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 ∆(G) ≥ 7, la(G) =[( ∆(G)) /2] if G has no 5-cycles with chords.