Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges of G with at most k colors. If โ(G) is the maximum degree of G, then no graph has a total โ-coloring, but Vizing conjectured that every graph has a total (โ + 2)-coloring. This Total Coloring Conjecture rem
Total colorings of planar graphs with large maximum degree
โ Scribed by Borodin, O. V.; Kostochka, A. V.; Woodall, D. R.
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 97 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
It is proved that a planar graph with maximum degree โ โฅ 11 has total (vertex-edge) chromatic number โ + 1.
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