Title of the course: Ramsey Numbers
Instructors: Prof. John Gimbel, Prof. Tınaz Ekim
Institution: University of Alaska, Boğaziçi University
Dates: 24-30 August 2026
Prerequisites: Graph Theory and/or Discrete Math background. It can be the Graph Theory lecture starting the week of August 17, or a thorough reading of Chapters 1, 2.1, 2.2, 3.1, 3.2 and 8 (first 3 pages) from R. Gould, Graph Theory (https://faculty.fiu.edu/~ramsamuj/graphtheory/grap_txt.html ). Knowledge of graph coloring, stable sets and cliques is fundamental. It is not necessary, but a brief knowledge of probability would be useful.
Level: Advanced undergraduate and graduate
Abstract: Ramsey numbers: introduction, pigeonhole principle, classical results and asymptotics. Extensions of Ramsey numbers: multiple colors, hypergraphs, graph Ramsey numbers. Applications to number theory and geometry (happy end problem). Defective Ramsey numbers: introduction and asymptotics. Defective Ramsey numbers in graph classes: exact approaches and computational aspects including graph enumeration.
Language: EN