In 1852, botanist Francis Guthrie noticed something peculiar as he was coloring a map of counties in England. Despite the counties’ meandering shapes and varied configurations, four colors were all he ...

Abstract: In this paper, a four-color coloring algorithm for maximal planar graphs with finite boundary is proposed, which aims to explore the four-color coloring method for complex planar graphs.

Take an outline map of the lower 48 U.S. states and four crayons. Can you shade in the map so that every state is a different color than each of its neighbors, without resorting to a fifth color? This ...