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.
-colouring outerplanar graphs with large girth
✍ Scribed by Frédéric Maffray; Ana Silva
- Book ID
- 113567600
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 298 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
Suppose G and H are graphs. We say G is H-colorable if there is a homomorphism (edge-preserving vertex mapping) from G to H. We say a graph G is uniquely H-colorable if there is an onto homomorphism c from G to H, and any other homomorphism from G to H is the composition o o c of c with an automorph
It is known that the Mycielski graph can be generalized to obtain an infinite family of 4-chromatic graphs with no short odd cycles. The first proof of this result, due to Stiebitz, applied the topological method of Lov~sz. The proof presented here is elementary combinatorial.