Extremal graph theory
（重定向自Extremal graph）
![The Turán graph T(n,r) is an example of an extremal graph. It has the maximum possible number of edges for a graph on n vertices without (r+1)-cliques. This is T(13,4).](/Images/godic/202501/12/Turan_13-4.svg5026.png")
Extremal graph theory is a branch of the mathematical field of graph theory. Extremal graph theory studies extremal (maximal or minimal) graphs which satisfy a certain property. Extremality can be taken with respect to different graph invariants, such as order, size or girth. More abstractly, it studies how global properties of a graph influence local substructures of the graph.