Let T be a tree with delta T being greater than or equal to k. Show that T has at least k end-vertices.

Note that delta T is the greatest vertex degree.

I believe that this can be solved using the Hand Shaking Lemma:

Assume that T has k end vertices, and T is of order n, then:

2e(T)= (sum of degs of verts of deg 1) + (sum of degs of verts of deg greater than 1)

2e(T) = k(1) + (n-k)(

this is where things stop.

what i was hoping to do was to continue on in this manner until it reduced to e(T)= n-1 which is a condition of trees, and would therefore show that the assumption was correct. This is just not working out. Any thoughts?