In this paper, we prove that any graph G with maximum degree ÁG ! 11 p 49À241AEa2, which is embeddable in a surface AE of characteristic 1AE 1 and satis®es jVGj b 2ÁGÀ5À2 p 6ÁG, is class one.
Face colorings of embedded graphs
✍ Scribed by Dan Archdeacon
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 498 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
We characterize those graphs which have at least one embedding into some surface such that the faces can be properly colored in four or fewer colors. Embeddings into both orientable and nonorientable surfaces are considered.
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