This phase II trial studies how well radiation therapy with or without cisplatin works in treating patients with stage III-IV squamous cell carcinoma of the head and neck who have undergone surgery. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. It is not yet known if radiation therapy is more effective with or without cisplatin in treating patients with squamous cell carcinoma of the head and neck.