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System of Distinct Representatives

  1. Oct 15, 2009 #1

    JJ6

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    1. The problem statement, all variables and given/known data

    I have the following graph theory problem:

    jP5w1.png

    2. Relevant equations

    The only theorem I know about SDRs is Hall's theorem:

    Let S_1, ... , S_k be finite sets. S_1, ... , S_k has an SDR if and only if the union of any n of the sets has at least n elements.

    3. The attempt at a solution

    I have no idea how to start. The only theorem we've gone over in class dealing with SDRs is Hall's, but I have no idea how to apply that.
     
  2. jcsd
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