What is the structure of an optimal Ramsey graph?
Science / Mathematics
The project will investigate the fundamental properties of connection networks, also known as graphs. According to Ramsey theory, specific patterns, such as fully connected or entirely disconnected groups, will inevitably appear in any sufficiently large graph. A central question is: how large can a graph be and still avoid such substructures? In other words, what is the maximum size of a graph that lacks these Ramsey-type patterns? This fundamental problem remains unsolved. Successful approaches to this challenge often involve constructing graphs at random, connecting points by chance, or using algebraic methods, such as solving polynomial equations. My research will pursue a relatively unexplored strategy that combines elements of randomness and algebraic structure to address this longstanding question.
Amount invested
Institutions
- Instituto de Matemática Pura e Aplicada
