低树宽图的线性树性

Pub Date : 2022-05-27 DOI:10.7151/dmgt.2456

Xiang Tan, Jian-Liang Wu

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引用次数: 1

摘要

摘要设G为树宽为k的图，证明了当k≤3且最大度Δ≥5，或k = 4且Δ≥9，或Δ≥4k−3且k≥5，则G的线性树性la(G)为≤≤Δ2²\left\lceil{{\Delta\over 2}} \right\rceil

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The Linear Arboricity of Graphs with Low Treewidth

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

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