 # Question: What Is Chromatic Number In Graph Theory?

## Why is coloring a graph necessary?

Actual colors have nothing at all to do with this, graph coloring is used to solve problems where you have a limited amount of resources or other restrictions.

Coloring here means attaching a “color” or a number to each vertice such that no two vertices with a connecting edge have the save value..

## What are the application of graph Colouring?

The graph coloring problem has huge number of applications. 1) Making Schedule or Time Table: Suppose we want to make am exam schedule for a university. We have list different subjects and students enrolled in every subject. Many subjects would have common students (of same batch, some backlog students, etc).

## What is graph coloring give an example?

Graph coloring is nothing but a simple way of labelling graph components such as vertices, edges, and regions under some constraints. In a graph, no two adjacent vertices, adjacent edges, or adjacent regions are colored with minimum number of colors. … A coloring is given to a vertex or a particular region.

## Is a graph 2 colorable?

A graph is 2-colorable if we can color each of its vertices with one of two colors, say red and blue, in such a way that no two red vertices are connected by an edge, and no two blue vertices are connected by an edge (a k-colorable graph is defined in a similar way).

## What is chromatic number of a graph explain with example?

The chromatic number, χ(G), of a graph G is the smallest number of colors for V(G) so that adjacent vertices are colored differently. The chromatic number, χ(Sk),of a surface Sk is the largest χ(G) such that G can be imbedded in Sk. We prove that six colors will suffice for every planar graph.

## How do you prove a graph is three colorable?

Definition 1 A graph G is 3-colorable if the vertices of a given graph can be colored with only three colors, such that no two vertices of the same color are connected by an edge. In other words given a graph we denote each vertices as vi and vj where i,j < n.

## What is the condition for proper coloring of a graph?

Explanation: The condition for proper coloring of graph is that two vertices which share a common edge should not have the same color. If it uses k colors in the process then it is called k coloring of graph.

## What is the chromatic number of a cycle graph?

The number of vertices in Cn equals the number of edges, and every vertex has degree 2; that is, every vertex has exactly two edges incident with it….Cycle graphChromatic number3 if n is odd 2 otherwiseChromatic index3 if n is odd 2 otherwiseSpectrum{2 cos(2kπ/n); k = 1, …, n}8 more rows

## What is the main idea of graph Colouring problem explain with example?

Graph coloring is the procedure of assignment of colors to each vertex of a graph G such that no adjacent vertices get same color. The objective is to minimize the number of colors while coloring a graph. The smallest number of colors required to color a graph G is called its chromatic number of that graph.

## What is a K4 graph?

K4 is a maximal planar graph which can be seen easily. In fact, a planar graph G is a maximal planar graph if and only if each face is of length three in any planar embedding of G. Corollary 1.8. 2: The number of edges in a maximal planar graph is 3n-6.

## Is a self loop a cycle?

A cycle in a graph is, according to Wikipedia, An edge set that has even degree at every vertex; also called an even edge set or, when taken together with its vertices, an even subgraph. … Therefore the self-loop is a cycle in your graph.

## What is a cycle graph theory?

In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices. A graph without cycles is called an acyclic graph.

## What is a simple cycle?

A simple cycle is a cycle with no repeated vertices (except for the beginning and ending vertex). Remark: If a graph contains a cycle from v to v, then it contains a simple cycle from v to v. … Connected Graphs. A graph G is called connected if there is a path between any two distinct vertices of G.

## Is the 2 coloring problem in P or in NP?

Since graph 2-coloring is in P and it is not the trivial language (∅ or Σ∗), it is NP-complete if and only if P=NP.

## What is the chromatic number of a tree?

Trees- A Tree is a special type of connected graph in which there are no circuits. Every tree is a bipartite graph. So, chromatic number of a tree with any number of vertices = 2.