Linear arboricity of 1-planar graphs

The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. In 1981, Akiyama, Exoo and Harary conjectured that [Delta(G)/2] <= la(G) <= [Delta(G)+1/2] for any simple graph G. A graph G is 1-planar if it can be drawn in the plane so that each edge has at most one crossing. In this paper, we confirm the conjecture for 1-planar graphs G with Delta(G) >= 13.