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Math Help - Graph Theory / Chromatic Number of a Complete Graph

  1. #1
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    Question 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?

    Thanks in advance!

    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?
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  2. #2
    MHF Contributor
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    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 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.
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