Why is the 4 Colour theorem important?

Why is the 4 Colour 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 proved the 4 color theorem?

A computer-assisted proof of the four color theorem was proposed by Kenneth Appel and Wolfgang Haken in 1976. Their proof reduced the infinitude of possible maps to 1,936 reducible configurations (later reduced to 1,476) which had to be checked one by one by computer and took over a thousand hours [1].

What are the four colours?

There are four psychological primary colours – blue, green, yellow and red.

Has the four-color theorem been solved?

The Four Colour Conjecture was first stated just over 150 years ago, and finally proved conclusively in 1976. It is an outstanding example of how old ideas combine with new discoveries and techniques in different fields of mathematics to provide new approaches to a problem.

What is map problem?

This maps problem concerns the extent to which spatial information and localization can satisfy the explanatory needs for perception and cognition. Several areas of investigation exemplify how the neural basis of speech and language is discussed in those terms (regions, streams, hemispheres, networks).

Can a non planar graph be 4 colorable?

3 Answers. Obviously not. A graph is bipartite if and only if it is 2-colorable, but not every bipartite graph is planar (K3,3 comes to mind).

What is the four-color map problem?

It was a kind of question that you didn’t want to attempt during an exam that you have ever taken during your life. Simply put, the Four-Color Map Problem is about finding the minimum number of different colors that you will need for the sake of coloring a map in a manner that no two adjacent regions feature the same color.

How many colors does it take to make a map?

… given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Adjacent means that two regions share a common boundary curve segment, not merely a corner where three or more regions meet.

Can a planar map be colored with just three colors?

While every planar map can be colored with four colors, it is NP-complete in complexity to decide whether an arbitrary planar map can be colored with just three colors. A cubic map can be colored with only three colors if and only if each interior region has an even number of neighboring regions.

What is the four color map theorem?

A four-coloring of a map of the states of the United States (ignoring lakes). In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color.