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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. Determine whether each of the following statements is true or false. ? ? ? ? ? 1. If every vertex of a graph has degree at most 4, then the chromatic index of the graph is at least 4. ✓2. If a graph contains a vertex of degree 10, then the chromatic index of the graph is at least 10. 3. In any bipartite graph G, X(G) = 2. ✓4. If a graph contains a vertex of degree 10, then the chromatic number of the graph is at least 10. ✓5. For all n > 3, x'(Cn) = A(Cn).

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. Determine whether each of the following statements is true or false. ? ? ? ? ? 1. If every vertex of a graph has degree at most 4, then the chromatic index of the graph is at least 4. ✓2. If a graph contains a vertex of degree 10, then the chromatic index of the graph is at least 10. 3. In any bipartite graph G, X(G) = 2. ✓4. If a graph contains a vertex of degree 10, then the chromatic number of the graph is at least 10. ✓5. For all n > 3, x'(Cn) = A(Cn).

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. Determine whether each of the following statements is true or false. ? ? ? ? ? 1. If every vertex of a graph has degree at most 4, then the chromatic index of the graph is at least 4. 2. If a graph contains a vertex of degree 10, then the chromatic index of the graph is at least 10. 3. In any bipartite graph G, X(G) = 2. 4. If a graph contains a vertex of degree 10, then the chromatic number of the graph is at least 10. 5. For all n > 3, x'(Cn) = A(Cn).
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. Determine whether each of the following statements is true or false. ? ? ? ? ? 1. If every vertex of a graph has degree at most 4, then the chromatic index of the graph is at least 4. 2. If a graph contains a vertex of degree 10, then the chromatic index of the graph is at least 10. 3. In any bipartite graph G, X(G) = 2. 4. If a graph contains a vertex of degree 10, then the chromatic number of the graph is at least 10. 5. For all n > 3, x'(Cn) = A(Cn).
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