Question

2
A)

What is the chromatic number of the 9-cycle C,?

B)

C)

Answer 1

(A)

If the cycle has an even degree, such as degree 4 or 6 or 8, then its chromatic number is 2.

If the cycle has an odd degree, such as degree 3 or 5 or 7 or 11, then its chromatic number is 3.

Therefore,the answer is 3.

(B)

chromatic number

2

As Kmn, m=n=3 : 2 (independent of , follows from being bipartite)

Therefore,the answer is 2.

(c)

A complete graph with n vertices is n-chromatic, because all its vertices are adjacent. So, χ(Kn) = n and χ(Kn) = 1. Therefore we see that a graph containing a complete graph of r vertices is at least r-chromatic. For example, every graph containing a triangle is at least 3-chromatic.

Therefore,the answer is 5.

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