## Abstract A face of an edge‐colored plane graph is called __rainbow__ if the number of colors used on its edges is equal to its size. The maximum number of colors used in an edge coloring of a connected plane graph __G__with no rainbow face is called __the edge‐rainbowness__ of __G__. In this pap
Colorings Of Plane Graphs With No Rainbow Faces
✍ Scribed by Veselin Jungić; Daniel Král’; Riste Škrekovski
- Book ID
- 106167588
- Publisher
- Springer-Verlag
- Year
- 2006
- Tongue
- English
- Weight
- 224 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
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## Abstract We study vertex‐colorings of plane graphs that do not contain a rainbow face, i.e., a face with vertices of mutually distinct colors. If __G__ is a 3 ‐connected plane graph with __n__ vertices, then the number of colors in such a coloring does not exceed $\lfloor{{7n-8}\over {9}}\rfloo
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