It is proved that if G is a planar graph with total (vertex-edge) chromatic number χ , maximum degree and girth g, then χ = + 1 if ≥ 5 and g ≥ 5, or ≥ 4 and g ≥ 6, or ≥ 3 and g ≥ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.
Fractional total colourings of graphs of high girth
✍ Scribed by Tomáš Kaiser; Andrew King; Daniel Králʼ
- Book ID
- 113698875
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 273 KB
- Volume
- 101
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open