Distance and Colorings
Gary Chartrand, Ping Zhang · 2019
The three most common types of colorings are proper colorings, rainbow colorings, and monochromatic colorings, where proper colorings are by far the best known and most studied. By the Four Color Theorem, the regions of every map, regardless of how many regions there may be, can be colored with four or fewer colors so that every two adjacent regions (regions sharing a common boundary) are assigned distinct colors. However, if a map contains a large number of regions, then it may be more appealing to use several colors to color the regions rather than trying to minimize the number of colors. A radio coloring of a dual planar graph is an assignment of colors to the vertices of the graph such that two colors can be assigned to two distinct vertices.