Geodesic
The linear arboricity of graphs with low treewidth
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 475-487

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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⌉.
Keywords: graph, minor, linear arboricity, linear forest, treewidth 
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Tan, Xiang; Wu, Jian-Liang. The linear arboricity of graphs with low treewidth. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 475-487. http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a3/