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,
See also Blue-Empty Graph, Extremal Graph, Monochromatic Forced Triangle
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.