Planar graphs without triangles adjacent to cycles of length from 4 to 7 are 3-colorable
β Scribed by O.V. Borodin; A.N. Glebov; A. Raspaud
- Book ID
- 108114224
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 468 KB
- Volume
- 310
- 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
If in a plane graph with minimum degree 2 3 no t w o triangles have an edge in common, then: (1 there are two adjacent vertices with degree sum at most 9, and (2) there is a face of size between 4 and 9 or a 10-face incident with ten 3-vertices. It follows that every planar graph without cycles betw