Editing Extremal graph theory (section)

===Forbidden subgraphs===
{{main|Forbidden subgraph problem}}

The '''forbidden subgraph problem''' is one of the central problems in extremal graph theory. Given a graph <math>G</math>, the forbidden subgraph problem asks for the maximal number of edges <math>\operatorname{ex}(n,G)</math> in an <math>n</math>-vertex graph that does not contain a subgraph isomorphic to <math>G</math>. 

When <math>G = K_r</math> is a complete graph, [[Turán's theorem]] gives an exact value for <math>\operatorname{ex}(n,K_r)</math> and characterizes all graphs attaining this maximum; such graphs are known as [[Turán graph|Turán graphs]]. 
For non-bipartite graphs <math>G</math>, the [[Erdős–Stone theorem]] gives an asymptotic value of <math>\operatorname{ex}(n, G)</math> in terms of the chromatic number of <math>G</math>. 
The problem of determining the asymptotics of <math>\operatorname{ex}(n, G)</math> when <math>G</math> is a [[bipartite graph]] is open; when <math>G</math> is a complete bipartite graph, this is known as the [[Zarankiewicz problem]].