A Planar Linear Arboricity Conjecture

The linear arboricity la(G) of a graph G is the minimum number of linear forests (graphs where every connected component is a path) that partition the edges of G. In 1984, Akiyama et al. [1] stated the Linear Arboricity Conjecture (LAC), that the linear arboricity of any simple graph of maximum degree ∆ is either ⌈ ⌉ ⌈ ⌉ ∆ ∆+1