What is four color theorem in graph theory?

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color. This problem is sometimes also called Guthrie’s problem after F. Guthrie, who first conjectured the theorem in 1852.

How do you know if a graph is 4-colorable?

A graph is said to be n-colorable if it’s possible to assign one of n colors to each vertex in such a way that no two connected vertices have the same color. Obviously the above graph is not 3-colorable, but it is 4-colorable.

Why is the 4 color theorem important?

The 4-color theorem is fairly famous in mathematics for a couple of reasons. First, it is easy to understand: any reasonable map on a plane or a sphere (in other words, any map of our world) can be colored in with four distinct colors, so that no two neighboring countries share a color.

Who Solved the 4 color problem?

The four-colour problem was solved in 1977 by a group of mathematicians at the University of Illinois, directed by Kenneth Appel and Wolfgang Haken, after four years of unprecedented synthesis of computer search and theoretical reasoning.

Is every 4 colorable graph planar?

The Four Color Theorem states that every planar graph is properly 4-colorable. Moreover, it is well known that there are planar graphs that are non-4 -list colorable.

Who made the four color theorem?

Without doubt, the Four-Color Theorem is one of the few mathematical problems in history whose origin can be dated precisely. Francis Guthrie (1831- 99), a student in London, first posed the conjecture in October, 1852, while he was coloring the regions on a map of England.

Who created the 4 color theorem?

Who Solved the four color theorem?

Guthrie’s question became known as the Four Color Problem, and it grew to be the second most famous unsolved problem in mathematics after Fermat’s last theorem. In 1976, two mathematicians at the University of Illinois, Kenneth Appel and Wolfgang Haken, announced that they had solved the problem.