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If a graph G is k-colorable and k<n, for any integer n then it is ___________ ans. n2 nodes (k3+n3+1) nodes n-colorable (k+n)-colorable

Question

If a graph G is k-colorable and k<n, for any integer n then it is ___________

ans.

  • n2 nodes
  • (k3+n3+1) nodes
  • n-colorable
  • (k+n)-colorable
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Solution

The text seems to be a part of a multiple-choice question related to graph theory in mathematics, but the question itself is not provided. However, I can explain the terms used:

  1. A graph G is k-colorable: This means that you can color the vertices of the graph with k different colors in such a way that no two adjacent vertices share the same color.

  2. k<n: This means that the number of colors used to color the graph is less than some integer n.

  3. n-colorable: This means that you can color the vertices of the graph with n different colors in such a way that no two adjacent vertices share the same color.

  4. (k+n)-colorable: This means that you can color the vertices of the graph with (k+n) different colors in such a way that no two adjacent vertices share the same color.

Without the actual question, it's hard to provide a specific answer. However, if a graph G is k-colorable and k<n, it doesn't necessarily mean it's n-colorable or (k+n)-colorable. It simply means that the graph can be colored with k colors. It could possibly be colored with more colors, but that would depend on the specific graph.

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