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Turán's theorem
Extremal graph theory bound on clique-free graph edges
Turán's theorem
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. It is one of the central results of extremal graph theory, an area studying the largest or smallest graphs with given properties, and is a special case of the forbidden subgraph problem on the maximum number of edges in a graph that does not have a given subgraph. An example of an n {\displaystyle n} -vertex graph that does not contain any ( r + 1 ) {\displaystyle (r+1)} -vertex clique K r + 1 {\displaystyle K_{r+1}} may be formed by partitioning the set of n {\displaystyle n} vertices into r {\displaystyle r}...
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