Extremal Graph Theory
Extremal Graph Theory focuses on determining the maximum or minimum number of edges in a graph that satisfies certain properties. It involves studying the extremal properties of graphs, such as the maximum number of edges a graph can have without containing a certain subgraph, or the minimum number of edges required for a graph to have a specific property. Extremal Graph Theory often involves proving the existence of graphs that achieve these extremal properties, as well as identifying the structure of optimal graphs.