Exercise 3.

For each degree sequence below, decide whether it must always, must never, or could possibly be a degree sequence for a tree. Justify your answers.

1. \(\displaystyle (3, 3, 2, 2, 2)\)

2. \(\displaystyle (3, 2, 2, 1, 1, 1)\)

3. \(\displaystyle (3, 3, 3, 1, 1, 1)\)

4. \(\displaystyle (4, 4, 1, 1, 1, 1, 1, 1)\)