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Graph Theory Proof

  1. Mar 25, 2009 #1
    1. Suppose a graph has nine vertices each of degree 5 or 6. Prove that at least five vertices have degree 6 or at least six vertices have degree 5.

    2. Relevant equations

    3. I'm pretty sure that I need to use the Pigeonhole Principle to solve, but don't know where to go from there.
  2. jcsd
  3. Mar 25, 2009 #2


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    Suppose the graph has fewer than 5 vertices of degree 6. How many vertices does that leave? What degree do those vertices have?
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