Answer to Question #306161 in Algebra for nicky

Question

Find all trees T where two-thirds of the vertices of T have degree 1 and the remaining one-third of the vertices have degree 3.

Answer 1

9. Find all trees T for which exactly two-thirds of the vertices have order 1 and the remaining one-third of the vertices have order 3 (of course the order must be divisible by 3). Prove that your list is complete. Hint: Start by finding all possible orders of T. There aren't many possibilities.