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 numbers of red and blue Triangles). Goodman (1959) showed that for an extremal graph,
See also Bichromatic Graph, Blue-Empty Graph, Goodman's Formula, Monochromatic Forced Triangle, Schwenk's Formula
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.
Sloane, N. J. A. Sequence
A014557
in ``The On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html.