# Turán graph

In

mathematical graph theory, the

**Turán graph** for given

natural numbers *n* and

*k*, denoted

*T*(

*n*,

*k*), is defined as the extremal graph with

*n* vertices which does not contain the

complete graph *K*_{k} as a subgraph. An upper bound for the number of edges of

*T*(

*n*,

*k*), typically written as

*t*(

*n*,

*k*), is given by

Turán's theorem; as a special case, for

*k* = 3, one obtains

Turán graphs were first described and studied by

Hungarian mathematician Paul Turán.