A Study to Assess Adjuvant Immunotherapy With Nivolumab Plus Relatlimab Versus Nivolumab Alone After Complete Resection of Stage III-IV Melanoma

Inclusion Criteria: * Must have been diagnosed with either Stage IIIA (\> 1 mm tumor in lymph node)/B/C/D or Stage IV melanoma by American Joint Committee on Cancer (AJCC) v8 and have histologically confirmed melanoma that is completely surgically resected (free of disease) with negative margins in order to be eligible * Participants ≥ 18 years of age must have an Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 1. Adolescent participants between 12 and \< 18 years of age must have a Lansky/Karnofsky performance score ≥ 80% * Complete resection must be performed within 90 days prior to randomization * All participants must have disease-free status documented by a complete physical examination within 14 days prior to randomization and imaging studies within 35 days prior to randomization * Tumor tissue must be provided for biomarker analyses Exclusion Criteria: * History of ocular melanoma * Untreated/unresected CNS metastases or leptomeningeal metastases * Active, known, or suspected autoimmune disease * Participants with serious or uncontrolled medical disorder * Prior immunotherapy treatment for any prior malignancy: No prior immunotherapies are permitted * Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection within 4 weeks prior to screening * History of myocarditis, regardless of etiology. Other protocol-defined inclusion/exclusion criteria apply