RT With or Without Cetuximab in Treating Patients Who Have Undergone Surgery for Locally Advanced Head and Neck Cancer

Conditions for Patient Eligibility: * Pathologically (histologically) proven diagnosis of squamous cell carcinoma (including variants such as verrucous carcinoma, spindle cell carcinoma, carcinoma NOS \[not otherwise specified\], etc.) of the head/neck (oral cavity, oropharynx or larynx); Note: Hypopharynx primaries are excluded because these patients have both a poor prognosis and high likelihood of post- radiation complications. * Clinical stage T1, N1-2 or T2-4a, N0-2, M0 including no distant metastases, based upon the following minimum diagnostic workup: * General history and physical examination by a radiation oncologist and/or medical oncologist within 8 weeks prior to registration; * Examination by an otolaryngologists or Head \& Neck Surgeon, within 8 weeks prior to registration; a laryngopharyngoscopy (mirror and/or fiberoptic and/or direct procedure) is recommended but not required. * Chest x-ray (at a minimum) or chest computed tomography (CT) scan (with or without contrast) or CT/positron emission tomography (PET) of chest (with or without contrast) within 8 weeks prior to registration. * Gross total resection of the primary tumor with curative intent must be completed within 7 weeks of registration with surgical pathology demonstrating one or more of the following intermediate risk factors: * Perineural invasion; * Lymphovascular invasion; * Single lymph node \> 3 cm or ≥ 2 lymph nodes (all \< 6 cm) \[no extracapsular extension\]; * Close margin(s) of resection, defined as cancer extending to within 5 mm of a surgical margin, and/or an initially focally positive margin that is subsequently superseded by intraoperative negative margins. Similarly, patients whose tumors had focally positive margins in the main specimen but negative margins from re-excised samples in the region of the positive margin are eligible. * Pathologically confirmed T3 or T4a primary tumor. * T2 oral cavity cancer with \> 5 mm depth of invasion. * Zubrod Performance Status of 0-1 within 2 weeks prior to registration; * Age ≥ 18; * Complete blood count (CBC)/differential obtained within 4 weeks prior to registration on study, with adequate bone marrow function defined as follows: * Absolute granulocyte count (AGC) ≥ 1,500 cells/mm3; * Platelets ≥ 100,000 cells/mm3; * Hemoglobin (Hgb) ≥ 8.0 g/dl (Note: The use of transfusion or other intervention to achieve Hgb ≥8.0 g/dl is acceptable). * Adequate hepatic function, defined as follows: * Total bilirubin \< 2 x institutional upper limit of normal (ULN) within 2 weeks prior to registration; * aspartate aminotransferase (AST) or alanine transaminase (ALT) \< 3 x institutional ULN within 2 weeks prior to registration. * Adequate renal function, defined as follows: * Serum creatinine (Scr) \< 2 x institutional ULN within 2 weeks prior to registration or; creatinine clearance (CCr) ≥ 50 ml/min within 2 weeks prior to registration determined by 24-hour collection or estimated by Cockcroft-Gault formula: CCr male = \[(140 - age) x (weight in kg)\] /\[(SCr mg/dl) x (72)\] CCr female = 0.85 x (CCr male) * Negative serum pregnancy test within 2 weeks prior to registration for women of childbearing potential; * The following assessments are required within 2 weeks prior to the start of registration: Na, K, Cl, glucose, Ca, Mg, and albumin. Note: Patients with an initial magnesium \< 0.5 mmol/L (1.2 mg/dl) may receive corrective magnesium supplementation but should continue to receive either prophylactic weekly infusion of magnesium and/or oral magnesium supplementation (e.g., magnesium oxide) at the investigator's discretion. * Women of childbearing potential and male participants who are sexually active must agree to use a medically effective means of birth control; * Patients must provide study specific informed consent prior to study entry, including consent for mandatory tissue submission for EGFR and for oropharyngeal patients, HPV analyses. Conditions for Patient Ineligibility * Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 3 years; noninvasive cancers (For example, carcinoma in situ of the breast, oral cavity, or cervix are all permissible) are permitted even if diagnosed and treated \< 3 years ago. Patients with simultaneous primaries or bilateral tumors are excluded, with the exception of patients with bilateral tonsil cancers or patients with T1-2, N0, M0 resected differentiated thyroid carcinoma, who are eligible. * Per the operative and/or pathology report, positive margin(s) \[defined as tumor present at the cut or inked edge of the tumor\], nodal extracapsular extension, and/or gross residual disease after surgery; Note: Patients whose tumors had focally positive margins in the main specimen but negative margins from re-excised samples in the region of the positive margin are eligible. * Prior systemic chemotherapy or anti-EGF therapy for the study cancer; note: prior chemotherapy or anti-EGF therapy for a different cancer is allowable. * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields; * Severe, active co-morbidity, defined as follows: * Unstable angina and/or congestive heart failure requiring hospitalization within 6 months prior to registration; * Transmural myocardial infarction within 6 months prior to registration; * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration; * Chronic Obstructive Pulmonary Disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of registration; * Idiopathic pulmonary fibrosis or other severe interstitial lung disease that requires oxygen therapy or is thought to require oxygen therapy within 1 year prior to registration; * Hepatic insufficiency resulting in clinical jaundice and/or coagulation defects; note, however, that laboratory tests for coagulation parameters are not required for entry into this protocol. * Acquired Immune Deficiency Syndrome (AIDS) based upon current Centers for Disease Control and Prevention (CDC) definition; note: HIV testing is not required for entry into this protocol. The need to exclude patients with AIDS from this protocol is necessary because the treatments involved in this protocol may be significantly immunosuppressive. Protocol-specific requirements may also exclude immuno-compromised patients. * Grade 3-4 electrolyte abnormalities (CTCAE v4): * Serum calcium (ionized or adjusted for albumin) \< 7 mg/dl (1.75 mmol/L) or \>12.5 mg/dl (\> 3.1 mmol/L) despite intervention to normalize levels; * Glucose \< 40 mg/dl (\< 2.2 mmol/L) or \> 250 mg/dl (\> 14mmol/L); * Magnesium \< 0.9 mg/dl (\< 0.4 mmol/L) or \> 3 mg/dl (\> 1.23 mmol/L) despite intervention to normalize levels; * Potassium \< 3.0 mmol/L or \> 6 mmol/L despite intervention to normalize levels; * Sodium \< 130 mmol/L or \> 155 mmol/L despite intervention to normalize levels. * Pregnancy or women of childbearing potential and men who are sexually active and not willing/able to use medically acceptable forms of contraception; this exclusion is necessary because the treatment involved in this study may be significantly teratogenic. * Prior allergic reaction to cetuximab.