## 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.

**Why is the four 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.

**How many colors can you use for this picture or map following the rules of the 4 color theorem?**

Although Heawood found the major flaw in Kempe’s proof method in 1890, he was unable to go on to prove the four colour theorem, but he made a significant breakthrough and proved conclusively that all maps could be coloured with five colours.

### How long did it take to prove the 4 colour map theorem?

[1]. 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 uses of colour?**

10 Reasons to Use Color

- Use color to speed visual search. Color coding often speeds up visual search.
- Use color to improve object recognition.
- Use color to enhance meaning.
- Use color to convey structure.
- Use color to establish identity.
- Use color for symbolism.
- Use color to improve usability.
- Use color to communicate mood.

**What is the main idea of graph coloring problem explain with example?**

Graph coloring problem is to assign colors to certain elements of a graph subject to certain constraints. Vertex coloring is the most common graph coloring problem. The problem is, given m colors, find a way of coloring the vertices of a graph such that no two adjacent vertices are colored using same color.

## What is Dirac’s theorem?

The classical Dirac theorem asserts that every graph G on n vertices with minimum degree \delta(G) \ge \lceil n/2 \rceil is Hamiltonian. The lower bound of \lceil n/2 \rceil on the minimum degree of a graph is tight.

**What are the four colors?**

Orange, Gold, Green, and Blue. Each color represents a different primary personality type, and all four lay the foundation of True Colors’ fun and insightful personality-identification system.