On 3-colorings of Plane Graphs
โ Scribed by Bao-gang Xu
- Book ID
- 106301025
- Publisher
- Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2004
- Tongue
- English
- Weight
- 162 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0168-9673
No coin nor oath required. For personal study only.
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## Abstract A __polychromatic k__โ__coloring__ of a plane graph __G__ is an assignment of __k__ colors to the vertices of __G__ such that every face of __G__ has __all k__ colors on its boundary. For a given plane graph __G__, one seeks the __maximum__ number __k__ such that __G__ admits a polychro
## Abstract We study vertexโcolorings 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 โconnected plane graph with __n__ vertices, then the number of colors in such a coloring does not exceed $\lfloor{{7n-8}\over {9}}\rfloo
Borodin, O.V., Cyclic coloring of plane graphs, Discrete Mathematics 100 (1992) 281-289. Let G be a plane graph, and let x,(G) be the minimum number of colors to color the vertices of G so that every two of them which lie in the boundary of the same face of the size at most k, receive different colo