## What is the rule for graph coloring?

As stated above, regular coloring is a rule for coloring graphs which states that no two adjacent vertices may have the same color. See Figure 10 for an example. In the figure, graph G is properly colored by regular coloring rules, while G is not, as it contains two adjacent vertices that are both colored with color R.

### What is the smallest number of colors needed for coloring the graph properly?

Chromatic Number: The smallest number of colors needed to color a graph G is called its chromatic number. For example, the following can be colored minimum 2 colors.

**What do the colors on the map mean?**

Physical maps use color most dramatically to show changes in elevation. A palette of greens often displays elevations. Dark green usually represents low-lying land, with lighter shades of green used for higher elevations. Green-gray, red, blue-gray, or some other color is used for elevations below sea level.

**What is map coloring problem?**

topological graph theory is the map-colouring problem. This problem is an outgrowth of the well-known four-colour map problem, which asks whether the countries on every map can be coloured by using just four colours in such a way that countries sharing an edge have different colours.

## How is graph theory used in colouring a map?

We have already used graph theory with certain maps. As we zoom out, individual roads and bridges disappear and instead we see the outline of entire countries. When colouring a map – or any other drawing consisting of distinct regions – adjacent countries cannot have the same colour.

### What does it mean to color the vertices of a graph?

In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring.

**Can a graph be colored with three colors?**

In general it can be difficult to show that a graph cannot be colored with a given number of colors, but in this case it is easy to see that the graph cannot in fact be colored with three colors, because so much is “forced”.

**Where does the Convention of graph coloring come from?**

The convention of using colors originates from coloring the countries of a map, where each face is literally colored. This was generalized to coloring the faces of a graph embedded in the plane. By planar duality it became coloring the vertices, and in this form it generalizes to all graphs.