Let t and n be

positive integers with t at least equal to 2, and n greater than
or equal to t. The maximum number of

edges of a

graph of order n that doesn't
contain a complete

subgraph of order t is

(n) - sigma {i = 1, t - 1} (n

*i*)

(2) (2)

where the n

*i* form a

partition of n into t-1 parts which are as equal
as possible.

Furthermore, the complete (t-1)-partite

graph with parts of size n1,n2,...nt-1
is the only

graph whose number of

edges is equal to the

bound above but
still doesn't contain a complete

subgraph of order t.

--back to

combinatorics--