Short Answer

What can be said about the chromatic number of a graph that has \({K_n}\)as a subgraph?

\(\chi \left( G \right) \ge n\)

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Note the given data

Given \({K_n}\)is a subgraph of the given graph G.

We need to find the chromatic number of the given graph under the given conditions.

Step 2: Definition

The chromatic number of a graph is the smallest number of colors that can be used in an edge coloring of the graph. The edge chromatic number of a graph is denoted by \(\chi \left( G \right)\)

Step 3: Calculation

As n colours are absolutely necessary to color \({K_n}\), it follows that the chromatic number \(\chi \left( G \right)\) must be at least n, as the number of vertices of G is at least n (since the vertices of \({K_n}\) is a subset of the vertices of G)

So \(\chi \left( G \right) \ge n\)

Hence solution is \(\chi \left( G \right) \ge n\)

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Discrete Mathematics and its Applications

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Short Answer

What can be said about the chromatic number of a graph that has \({K_n}\)as a subgraph?

Step by Step Solution

Step 1: Note the given data

Step 2: Definition

Step 3: Calculation

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Discrete Mathematics and its Applications

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Short Answer

What can be said about the chromatic number of a graph that has \({K_n}\)as a subgraph?

Step by Step Solution

Step 1: Note the given data

Step 2: Definition

Step 3: Calculation

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