What does the 4 color theorem state?
The four color theorem, or the four color map theorem, states that given any separation of the plane into contiguous regions, called a “map”, the regions can be colored using at most four colors so that no two adjacent regions have the same color.
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.
Is the four color theorem solved?
Four-colour map problem, problem in topology, originally posed in the early 1850s and not solved until 1976, that required finding the minimum number of different colours required to colour a map such that no two adjacent regions (i.e., with a common boundary segment) are of the same colour.
What are the possible application of the four color theorem?
One of the 4 Color Theorem most notable applications is in mobile phone masts. These masts all cover certain areas with some overlap meaning that they can’t all transmit on the same frequency. A simple method of ensuring that no two masts that overlap have the same frequency is to give them all a different frequency.
What are the 4 colors?
That’s why it could be said that for our vision, there are four primary colors: red, green, yellow and blue.
Are all 4 colorable graphs 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.
Can you paint a plane using 2 colors so that any 2 points?
No you can’t, because there are three points that are vertexes of an equilateral triangle with a side of 10cm and you can’t have all 3 vertex colored differently.
Who is the Prince of India mathematics?
SRINIVASA RAMANUJAN 1887-1920 Ramanujan is India’s best mathematician ever. His main contributions are to the theory of numbers and mathematical analysis.
What is 4 color problem in graph theory?
In graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the same color, or for short: Every planar graph is four-colorable.
What is the four color theorem?
Four-Color Theorem. 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.
What is a simple proof of the four color theorem?
A simpler proof of the four color theorem is presented. The proof was reached using a series of equivalent theorems. First the maximum number of edges of a planar graph is obatined as well as the minimum number of edges for a complete graph. Then it is shown that for the theorem to be false there must exist a complete planar
How was the four colour theorem proved?
The four color theorem was proved in 1976 by Kenneth Appel and Wolfgang Haken after many false proofs and counterexamples (unlike the five color theorem, a theorem that states that five colors are enough to color a map, which was proved in the 1800s). Sep 20 2019
How does the four color map theorem relate to math?
In mathematics, the four color theorem, or the four color map theorem, states that, 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.
