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.