Extremal graph theory

Extremal graph theory is a branch of mathematics that studies how the properties of graphs (collections of points connected by lines) change when limiting conditions are applied. It seeks to determine the maximum or minimum number of edges a graph can have without containing certain subgraphs (specific arrangements of points and lines). Essentially, it explores the balance between structure and constraints, helping us understand the limits of connectivity in graphs. This theory has applications in computer science, network design, combinatorial optimization, and more, influencing how we analyze complex systems and relationships.