Non-rainbow colorings of 3-, 4- and 5-connected plane graphs

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 7n−8 9 . If G is 4-connected, then the number of colors is at most 5n−6 8 , and for n ≡ 3 (mod 8), it is at most 5n−6

• Type: Journal
• Year: 2010
• Where: JGT
• Authors: Zdenek Dvorak, Daniel Král', Riste Skrekovski
• Keywords: 3-connected Plane Graph, Distinct Colors, JGT 2010, Plane Graph