Chromatic Edges 1 0 10

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An edge coloring with k colors is called a k-edge-coloring and is equivalent to the problem of partitioning the edge set into k matchings. The smallest number of colors needed for an edge coloring of a graph G is the chromatic index, or edge chromatic number, χ′(G). A Tait coloring is a 3-edge coloring of a cubic graph. JixiPix takes vintage to a whole new extreme. JixiPix Chromatic Edges Overview Gone are the days of having a few tiny choices when it comes to adding. JixiPix takes vintage to a whole new extreme. JixiPix Chromatic Edges Overview Gone are the days of having a few tiny choices when it comes to adding.

Graph Coloring-

• Graph Coloring is also called as Vertex Coloring.
• It ensures that there exists no edge in the graph whose end vertices are colored with the same color.
• Such a graph is called as a Properly colored graph.

Graph Coloring Example-

The following graph is an example of a properly colored graph-

In this graph,

• No two adjacent vertices are colored with the same color.
• Therefore, it is a properly colored graph.

Graph Coloring Applications-

Some important applications of graph coloring are as follows-

• Map Coloring
• Scheduling the tasks
• Preparing Time Table
• Assignment
• Conflict Resolution
• Sudoku

Chromatic Number-

Chromatic Number Example-

Consider the following graph-

In this graph,

• No two adjacent vertices are colored with the same color.
• Minimum number of colors required to properly color the vertices = 3.
• Therefore, Chromatic number of this graph = 3.
• We can not properly color this graph with less than 3 colors.

Also Read-Types of Graphs in Graph Theory

Chromatic Number Of Graphs-

Chromatic Number of some common types of graphs are as follows-

1. Cycle Graph-

• A simple graph of ‘n' vertices (n>=3) and ‘n' edges forming a cycle of length ‘n' is called as a cycle graph.
• In a cycle graph, all the vertices are of degree 2.

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Examples-

2. Planar Graphs-

A Planar Graph is a graph that can be drawn in a plane such that none of its edges cross each other.

Examples-

• All the above cycle graphs are also planar graphs.
• Chromatic number of each graph is less than or equal to 4.

3. Complete Graphs-

• A complete graph is a graph in which every two distinct vertices are joined by exactly one edge.
• In a complete graph, each vertex is connected with every other vertex.
• So to properly it, as many different colors are needed as there are number of vertices in the given graph.

Examples-

4. Bipartite Graphs-

• A Bipartite Graph consists of two sets of vertices X and Y.
• The edges only join vertices in X to vertices in Y, not vertices within a set.

Example-

5. 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.

Examples-

To gain better understanding about Graph Coloring & Chromatic Number,

Next Article-Graph Coloring Algorithm

Get more notes and other study material of Graph Theory.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Graph Coloring-

• Graph Coloring is also called as Vertex Coloring.
• It ensures that there exists no edge in the graph whose end vertices are colored with the same color.
• Such a graph is called as a Properly colored graph.

Graph Coloring Example-

The following graph is an example of a properly colored graph-

In this graph,

• No two adjacent vertices are colored with the same color.
• Therefore, it is a properly colored graph.

Graph Coloring Applications-

Some important applications of graph coloring are as follows-

• Map Coloring
• Scheduling the tasks
• Preparing Time Table
• Assignment
• Conflict Resolution
• Sudoku

Chromatic Number-

Chromatic Number Example-

Daz studio pro 4 10. Consider the following graph-

In this graph,

• No two adjacent vertices are colored with the same color.
• Minimum number of colors required to properly color the vertices = 3.
• Therefore, Chromatic number of this graph = 3.
• We can not properly color this graph with less than 3 colors.

Also Read-Types of Graphs in Graph Theory

Chromatic Number Of Graphs-

Chromatic Number of some common types of graphs are as follows-

1. Cycle Graph-

• A simple graph of ‘n' vertices (n>=3) and ‘n' edges forming a cycle of length ‘n' is called as a cycle graph.
• In a cycle graph, all the vertices are of degree 2.

Examples-

2. Planar Graphs-

A Planar Graph is a graph that can be drawn in a plane such that none of its edges cross each other.

Examples-

• All the above cycle graphs are also planar graphs.
• Chromatic number of each graph is less than or equal to 4.

3. Complete Graphs-

• A complete graph is a graph in which every two distinct vertices are joined by exactly one edge.
• In a complete graph, each vertex is connected with every other vertex.
• So to properly it, as many different colors are needed as there are number of vertices in the given graph.

Examples-

4. Bipartite Graphs-

• A Bipartite Graph consists of two sets of vertices X and Y.
• The edges only join vertices in X to vertices in Y, not vertices within a set.

Example-

5. 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.

Chromatic Edges 1 0 100

Chromatic Edges 1 0 101

Examples-

To gain better understanding about Graph Coloring & Chromatic Number,

Next Article-Graph Coloring Algorithm

Get more notes and other study material of Graph Theory.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Chromatic Edges 1 0 10 10 M To Inches

Chromatic Edges 1 0 105