An edge-face coloring of a plane graph with edge set E and face set F is a coloring of the elements of E ∪F so that adjacent or incident elements receive different colors. Borodin [Discrete Math 128(1-3): [21][22][23][24][25][26][27][28][29][30][31][32][33] 1994] proved that every plane graph of max
Every Plane Graph of Maximum Degree 8 has an Edge-Face 9-Coloring
✍ Scribed by Kang, Ross J.; Sereni, Jean-Sébastien; Stehlík, Matěj
- Book ID
- 118197854
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2011
- Tongue
- English
- Weight
- 294 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0895-4801
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract Chen et al., conjectured that for __r__≥3, the only connected graphs with maximum degree at most __r__ that are not equitably __r__‐colorable are __K__~__r, r__~ (for odd __r__) and __K__~__r__ + 1~. If true, this would be a joint strengthening of the Hajnal–Szemerédi theorem and Brooks
In this paper, we prove that any edge-coloring critical graph G with maximum degree ¿ (11 + √ 49 -24 )=2, where 6 1, has the size at least 3(|V (G)| -) + 1 if 6 7 or if ¿ 8 and |V (G)| ¿ 2 --4 -( + 6)=( -6), where is the minimum degree of G. It generalizes a result of Sanders and Zhao.