A two-coloring of a complete graph 
of 
nodes which contains exactly the number of monochromatic
forced triangles and no more (i.e., a minimum of 
where 
and 
are the number of red and blue triangles)
is called an extremal graph. Goodman (1959) showed
that for an extremal graph,
 |
(1)
|
Schwenk (1972) rewrote the equation in the form
 |
(2)
|
where 
is a binomial coefficient and 
is the floor function.
