1. Let F be a forest with n vertices and k connected components, with 1 deg(v) in terms of n and k. veV (F) (b) Show that the average degree of a vertex in F is strictly less than 2. (c) Conclude that...

1. Let F be a forest with n vertices and k connected components, with 1 ≤ k ≤ n.
(a) Compute X
v∈V (F)
deg(v) in terms of n and k.
(b) Show that the average degree of a vertex in F is strictly less than 2.
(c) Conclude that forests have leaves.

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