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This short course lecture, delivered by Alex Scott from the University of Oxford, explores the Erdős-Hajnal Conjecture as part of the 2nd Brazilian School of Combinatorics (EBC) organized by the Instituto de Matemática Pura e Aplicada. Delve into this fundamental problem in combinatorial mathematics during this 89-minute session, which represents the first installment of Scott's mini-course. The 2nd EBC, scheduled for March 10-14, 2025, in Rio de Janeiro, follows the successful format of the first edition that attracted 87 participants from 8 Brazilian states and 10 countries. The event features 11 plenary talks, 2 mini-courses, and daily poster presentations, providing an excellent opportunity for researchers and students to collaborate on open problems in combinatorics.
