# Thread: Graph Theory / Chromatic Number of a Complete Graph

1. ## Graph Theory / Chromatic Number of a Complete Graph

Hello all!

I have a question regarding the process for finding the chromatic number of a complete graph contraining 16 vertices. I know how to do it the 'brute force' way in which you manually draw and count each unique edge within the graph, but for a 16 vertice graph this is rather difficult.

Google has failed to yield any sort of formula for simplifying this, does any have any idea where I should go from here?

PS - Forgive me if this is the wrong section for this, but I also have another question on probability :

Suppose you flip a coin 3 times. What is the probability that exactly 1 of your flips were heads?

I think I'm merely over thinking this seemingly simple problem, can anyone point me in the right direction here?

2. ## Re: Graph Theory / Chromatic Number of a Complete Graph

Welcome to the forum.

I have a question regarding the process for finding the chromatic number of a complete graph contraining 16 vertices.
In a complete graph, each vertex is adjacent to every other vertex, so they all have to have different colors.

Suppose you flip a coin 3 times. What is the probability that exactly 1 of your flips were heads?
The total number of outcomes is $\displaystyle 2^3$. There are 3 successful outcomes, where the head occurs during the first, second, and third flip, respectively, and the other two flips return tails.