Hello all, This is the presentation of Graph Colouring in Graph theory and application. Use this presentation as a reference if you have any doubt you can comment here.

1. Graph Coloring
By
M. Baranitharan
Computer Science and Engineering

2. What is Graph Coloring?
Graph Coloring is an assignment of colors (or any distinct
marks) to the vertices of a graph. Strictly speaking, a coloring
is a proper coloring if no two adjacent vertices have the same
color

3. Origin of Problem

4. Why Graph Coloring?
• Many problems can be formulated as a graph coloring problem
including Time Tabling, Scheduling, Register Allocation, Channel
Assignment
• A lot of research has been done in this area so much is already
known about the problem space.

5. Origin
 Coloring theory started with the problem of coloring the
countries of a map in such a way that no two countries that
have a common border receive the same color.
 If we denote the countries by points in the plane and
connect each pair of points that correspond to countries with
a common border by a curve, we obtain a planar graph.

6. Map of the countries

7. Assume

8. Vertex Coloring
Vertex Coloring: It is a way of coloring the vertices of a graph
such that no two adjacent vertices share the same color.

9. Edges Coloring
An edge coloring assigns a color to each edge so that no two
adjacent edges share the same color.

10. Face Coloring
A face coloring of a planar graph assigns a color to each face
or region so that no two faces that share a boundary have
the same color.

11. Chromatic number
The chromatic number of a graph is the minimum number of
colors in a proper coloring of that graph. If chromatic
number is r then the graph is r-chromatic.
Chromatic number: 4

12. Chromatic Polynomial
Polynomial which gives the number of ways of proper coloring a
graph using a given number of colors
Ci = no. of ways to properly color a graph using exactly i colors
λ = total no of colors
λ Ci = selecting I colors out of λ colors
ΣCi
λ Ci = total number of ways a graph can be properly colored
using λ or lesser no. of colors
Pn(λ) of G = ΣCi
λ Ci

13. Applications

14. Thank you