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The following statements are about the chromatic number x(G) and the chromatic index x'(G) of graphs. We use A(G) for the maximum degree of G. Are the following statements true or false? ? ? 1. x'(G) ≥ A(G). 2. For all n ≥ 3, x'(Pn) = A(Pn). 3. For any cycle, the chromatic index is equal to the chromatic number. 4. The chromatic index of any planar graph is at most 4.

The following statements are about the chromatic number x(G) and the chromatic index x'(G) of graphs. We use A(G) for the maximum degree of G. Are the following statements true or false? ? ? 1. x'(G) ≥ A(G). 2. For all n ≥ 3, x'(Pn) = A(Pn). 3. For any cycle, the chromatic index is equal to the chromatic number. 4. The chromatic index of any planar graph is at most 4.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The following statements are about the chromatic number x(G) and the chromatic index x'(G) of graphs. We use A(G) for the maximum degree of G. Are the following statements true or false? ? ? ? ? 1. x'(G) ≥ A(G). 2. For all n ≥ 3, x'(Pn) = ▲(Pn). 3. For any cycle, the chromatic index is equal to the chromatic number. 4. The chromatic index of any planar graph is at most 4.
Transcribed Image Text:The following statements are about the chromatic number x(G) and the chromatic index x'(G) of graphs. We use A(G) for the maximum degree of G. Are the following statements true or false? ? ? ? ? 1. x'(G) ≥ A(G). 2. For all n ≥ 3, x'(Pn) = ▲(Pn). 3. For any cycle, the chromatic index is equal to the chromatic number. 4. The chromatic index of any planar graph is at most 4.
What is the chromatic index of each graph? P8 CA Cg K11,14 K14 -D
Transcribed Image Text:What is the chromatic index of each graph? P8 CA Cg K11,14 K14 -D
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