The linear arboricity of [formula omitted]-minor free graphs.

The linear arboricity l a (G) of a graph G is the minimum number of linear forests which partition the edges of G. In 1980, Akiyama et al. conjectured that for any graph G , ⌈ Δ (G) 2 ⌉ ≤ l a (G) ≤ ⌈ Δ (G) + 1 2 ⌉. In the paper, we establish two essential structural properties of K 5 -minor free graphs G , one is used to confirm the conjecture for all K 5 -minor free graphs, the other is devoted to proving that l a (G) = ⌈ Δ (G) 2 ⌉ holds if Δ (G) ≥ 9. In addition, we prove here that if G is a K 5 − -minor free graph and Δ (G) ≥ 5 , then l a (G) = ⌈ Δ (G) 2 ⌉. [ABSTRACT FROM AUTHOR]