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The Linear Arboricity of Planar Graphs without 5-, 6-Cycles with Chords |
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| Authors: | Hongyu Chen Xiang Tan Jianliang Wu Guojun Li |
| Institution: | 1. School of Science, Shanghai Institute of Technology, Shanghai, 201418, People’s Republic of China 2. School of Statistics and Mathematics, Shandong University of Finance, Jinan, 250014, Shandong, People’s Republic of China 3. School of Mathematics, Shandong University, Jinan, 250100, Shandong, People’s Republic of China |
| Abstract: | The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. In this paper, it is proved that for a planar graph G, ${la(G)=\lceil\frac{\Delta(G)}{2}\rceil}$ if Δ(G) ≥ 7 and G has no 5-cycles with chords, or Δ(G) ≥ 5 and G has no 5-, 6-cycles with chords. |
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