The Linear Arboricity of Graphs with Low Treewidth

Abstract

Abstract Let G be a graph with treewidth k. In the paper, it is proved that if k ≤ 3 and maximum degree Δ ≥ 5, or k = 4 and Δ ≥ 9, or Δ ≥ 4k − 3 and k ≥ 5, then the linear arboricity la(G) of G is ⌈ Δ2 ⌉ \left\lceil {{\Delta \over 2}} \right\rceil