the following statements are about the chromatic number g and the chromatic index g of graphs we

Name: the following statements are about the chromatic number g and the chromatic index g of graphs we use g for the maximum degree of g are the following statements true or false 1 if a graph con 70256
Uploaded: 2022-06-07T07:38:52-08:00
Duration: 4 min 3 s
Channel: Shaiju T
Description: the following statements are about the chromatic number g and the chromatic index g of graphs we use g for the maximum degree of g are the following statements true or false 1 if a graph con 70256

Step 1: Statement 1 states that if a graph contains a vertex of degree 7, then the chromatic ind

Question

The following statements are about the chromatic number χ(G) and the chromatic index χ′(G) of graphs. We use Δ(G) for the maximum degree of G. Are the following statements true or false? 1. If a graph contains a vertex of degree 7, then the chromatic index of the graph is at least 7. 2. For all n≥3, χ′(Cn)=Δ(Cn). 3. For any cycle, the chromatic index is equal to the chromatic number. 4. If every vertex of a graph has a degree at most 5, then the chromatic index of the graph is at least 5.

          The following statements are about the chromatic number χ(G) and the chromatic index χ′(G) of graphs. We use Δ(G) for the maximum degree of G. Are the following statements true or false?

1. If a graph contains a vertex of degree 7, then the chromatic index of the graph is at least 7.
2. For all n≥3, χ′(Cn)=Δ(Cn).
3. For any cycle, the chromatic index is equal to the chromatic number.
4. If every vertex of a graph has a degree at most 5, then the chromatic index of the graph is at least 5.

Added by Luz S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

06/07/2022

Step 1

This statement is true because the chromatic index of a graph is always greater than or equal to the maximum degree of the graph. Therefore, this statement is true. Show more…

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The following statements are about the chromatic number χ(G) and the chromatic index χ′(G) of graphs. We use Δ(G) for the maximum degree of G. Are the following statements true or false? 1. If a graph contains a vertex of degree 7, then the chromatic index of the graph is at least 7. 2. For all n≥3, χ′(Cn)=Δ(Cn). 3. For any cycle, the chromatic index is equal to the chromatic number. 4. If every vertex of a graph has a degree at most 5, then the chromatic index of the graph is at least 5.