Extremal Problems

We plan to continue our research in the area of extremal discrete mathematics. The central question of this field has the following form: determine the maximum (or minimum) size of a discrete mathematical object that satisfies a certain condition. It turns out that this general topic has connections to very diverse fields (geometry, design theory, number theory, algebra, topology, etc.) and to areas with important concrete applications in everyday life (computer science, coding theory, cryptography, optimization and scheduling problems, communication and networking problems, etc.). In particularly, we focus to the following questions in this project.

1. Ramsey numbers
2. Vertex partitions by monochromatic graphs
3. Transversals of highly intersecting d-track intervals
4. Alternating 4-paths in proper edge colorings