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On the vertex-arboricity of planar graphs without 7-cycles

✍ Scribed by Danjun Huang; Wai Chee Shiu; Weifan Wang


Book ID
113567658
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
965 KB
Volume
312
Category
Article
ISSN
0012-365X

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## Abstract It is known that not all planar graphs are 4‐choosable; neither all of them are vertex 2‐arborable. However, planar graphs without 4‐cycles and even those without 4‐cycles adjacent to 3‐cycles are known to be 4‐choosable. We extend this last result in terms of covering the vertices of a

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The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured for any simple graph G with maximum degree βˆ†. The conjecture has been proved to be true for graphs having βˆ† =