Linear arboricity of graphs with large minimum degree

In 1980, Akiyama, Exoo, and Harary conjectured that any graph G can be decomposed into at most (Δ(G)+1)/2 linear forests. We confirm the conjecture for sufficiently large graphs with large minimum degree. Precisely, we show that for any given 0<ε <1, there exists n₀ ∈ N for which the following statement holds: If G is a graph on n≥ n₀ vertices of minimum degree at least (1+ε )n/2, then G can be decomposed into at most (Δ(G)+1)/2 linear forests.