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 $\lceil {\Delta {({G})}\over {2}}\rceil \leq {la}({G}) \leq \lceil {\Delta({G})+{1}\over {2}}\rceil$ for any simple graph G. Wu wu proved the conjecture for a planar graph G of maximum degree $\Delta\not={{7}}$ . It is noted here that the conjecture is also true for $\Delta={{7}}$ . © 2008 Wiley Periodicals, Inc. J Graph Theory 58:210‐220, 2008