The linear arboricity of planar graphs with no short cycles

The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that for any simple graph G. In the paper, it is proved that if G is a planar graph with Δ≥7 and without i-cycles for some i∈{4,5}, then .