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Let f : [n] ? [n] be a function and let Tf be a labeled tree...

Let f : [n] ? [n] be a function and let Tf be a labeled tree on n vertices, constructed from f using the procedure demonstrated in class. Suppose that f takes exactly k different values. Show that Tf has at most n?k vertices with degree at least four.

Hint: First, determine the maximum number of leaves in Tf .

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