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Math Help - Tree Proof

  1. #1
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    Tree Proof

    Show that for every choice of n and x with n > x > 1 there is a tree on n vertices
    with maximum degree x that has exactly x leaves.

    Any advice? I'm at a loss... Thanks!
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Show that for every choice of n and x with n > x > 1 there is a tree on n vertices
    with maximum degree x that has exactly x leaves.

    Any advice? I'm at a loss... Thanks!
    The question itself, based on a few drawings on paper I think for (n,x) = (n,n-1) you can use the graph that has a single root connected to all leaves, and then for getting (n+1,n-1), just take one of the branches and put an intermediate vertex which will have degree two, which process can be continued indefinitely.

    Illustration for x = 4.
    Attached Thumbnails Attached Thumbnails Tree Proof-treenx1.png  
    Last edited by mr fantastic; September 22nd 2010 at 11:12 PM.
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