The regulating center for swallowing and vomiting in the human brain is the Medulla Oblongata. This is located in the lower part of the brainstem, which connects to the spinal cord. The Medulla Oblongata plays a crucial role in controlling various involuntary functions of the body, including swallowing and vomiting. It receives sensory information from the mouth and throat, and then sends signals to the muscles involved in these actions.

Let`s analyze the other options to understand why they are not the correct answers:

1) Cerebellum: The cerebellum is primarily responsible for coordinating movement, balance, and posture.

2) Cerebrum: The cerebrum is responsible for higher cognitive functions, such as thinking, memory, and perception.

4) Pons: The pons is involved in the control of breathing and serves as a relay center between the cerebrum and cerebellum.

Therefore, the correct answer is option 3, the Medulla Oblongata.