Advances in graph Ramsey theory

This project aims to solve significant questions at the forefront of graph amsey theory. Major progress is anticipated on the recently introduced concept of Ramsey equivalence, which includes the development of deep new tools that combine probabilistic methods, extremal graph theory, and graph decomposition techniques. These new tools are then utilised to solve old questions on the structure of minimal Ramsey graphs. Graph theory is a fundamental discipline within discrete mathematics that provides the theoretical background for understanding networks that are omnipresent in the modern world. Ramsey theory is the most celebrated part of graph theory with connections to number theory, geometry, analysis, logic, and computer science.