On some properties of 4‐regular plane graphs
Mirko Horňák, Stanislav Jendrol′ · Journal of Graph Theory · 1995
Abstract The d ‐distance face chromatic number of a connected plane graph is the minimum number of colors in such a coloring of its faces that whenever two distinct faces are at the distance at most d , they receive distinct colors. We estimate 1‐distance chromatic number for connected 4‐regular plane graphs. We show that 0‐distance face chromatic number of any connected multi‐3‐gonal 4‐regular plane graphs is 4. © 1995, John Wiley & Sons, Inc.