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,

Schwenk (1972) rewrote the equation in the form

where is a Binomial Coefficient and is the Floor Function.

**References**

Goodman, A. W. ``On Sets of Acquaintances and Strangers at Any Party.'' *Amer. Math. Monthly* **66**, 778-783, 1959.

Schwenk, A. J. ``Acquaintance Party Problem.'' *Amer. Math. Monthly* **79**, 1113-1117, 1972.

© 1996-9

1999-05-25