On the vertex-arboricity of planar graphs without 7-cycles
β 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 4βchoosable; neither all of them are vertex 2βarborable. However, planar graphs without 4βcycles and even those without 4βcycles adjacent to 3βcycles are known to be 4βchoosable. We extend this last result in terms of covering the vertices of a
## Abstract We prove in this note that the linear vertexβarboricity of any planar graph is at most three, which confirms a conjecture due to Broere and Mynhardt, and others.
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 β. The conjecture has been proved to be true for graphs having β =