It is proved that if G is a planar graph with total (vertex-edge) chromatic number Ο , maximum degree and girth g, then Ο = + 1 if β₯ 5 and g β₯ 5, or β₯ 4 and g β₯ 6, or β₯ 3 and g β₯ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.
Infinite highly connected planar graphs of large girth
β Scribed by A. Georgakopoulos
- Publisher
- Vandenhoeck & Ruprecht
- Year
- 2006
- Tongue
- German
- Weight
- 463 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0025-5858
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