Graph coloring
Definition :
It is a process or procedure of assigning colors to each corner or vertex in a particular graph in such a way that no particular adjacent vertices or corners get the same color.
It’s main objective is to reduce the amount of colors or number of colors while coloring in a given graph.
Vertex coloring is used efficiently and therefore is used more often. There are other graph coloring methods like Edge Coloring and Face Coloring which can be transformed into a vertex coloring method.
Edge Coloring :
Where none of the vertex is adjacent to two edge of the same color.
Face Coloring :
Or the other name is Geographical Map Coloring, used for geographical purposes.
Chromatic number of the graph :
It is the smallest number of colors that is required for coloring a graph.
How to Color a Graph :
We should follow the steps given below to color a given graph :
- Firstly, arrange the given vertices of the given graph in a particular order.
- Then, select the first corner and color it with the first color.
- Similarly, select the next vertex and color it with the color that is lowest numbered which has not been used as a color on any of the corners and if all the vertices are colored with similar color then introduce a new color to it. Keep repeating these steps unless all the vertices are colored properly.
Applications of the Graph Coloring :
- Used in creating schedule or timetable: Every problem or important thing can be highlighted or represented using a graph where each vertex is a particular subject. Therefore, it will be a graph coloring method where the least number of slots of time is used and is equal to a chromatic number of the given graph.
- Used in digital equipment such as Mobile Radio Frequency Assessment: When a particular type of frequency is assigned to the tower, the other tower towers must have different frequencies in that particular location. So, in order to assign frequencies and a minimum number of frequencies can be represented using graph coloring, where each tower will represent a corner or vertex and the edge between the two towers can be represented as the range for each other.
- Most widely used in Register Allocation: While optimization process in a compiler, the register allocation is a type of process for assigning a huge number of program target variables upon the least number of CPU registers. It is also a method of graph coloring.
- Used in Bipartite Graphs: It can be used to check if a given graph is a Bipartite graph or not by using two colors to color the graph. If that given graph is two colorable then that graph is Bipartite else it’s not.
- Used in Map coloring: widely used for geographical purposes for geographical maps of different countries where no same state or country can have a similar color. In short four colors are enough to color a given map.
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