The linear arboricity of planar graphs of maximum degree seven is four

The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama et al. conjectured that (G) 2 ≤ la(G) ≤ (G)+1 2 for any simple graph G. Wu [5] proved the conjecture for a planar graph G of maximum degree = 7. It is noted here that the conjecture is also true for = 7. © 2008 Wiley Periodicals, Inc. J Graph Theory