The relationship between the maximum average degree and the linear arboricity of a graph
Jianliang Wu · Journal of Shandong University · 2005
LetGbe a simple graph.Its maximumaverage degree mad(G) =max{2|E(H)|/|V(H)| :His a nonempty sub-graph ofG}.ThenGhasthelinear arboricityla(G) =「Δ(G)/2﹁ifΔ(G)≥ 7 and mad(G)≤ 4,orΔ(G) 5 and mad(G) 18/5,orΔ(G) ≥3 and mad(G) 3.