Extremal Graph
A two-coloring of a Complete Graph 
of 
nodes which contains exactly the number 
ofMonochromatic 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,
This is sometimes known as Goodman's Formula. Schwenk (1972) rewrote it in the form
sometimes known as Schwenk's Formula, where
is the Floor Function. The first few values of 
for 
, 2, ... are 0, 0, 0, 0, 0, 2, 4, 8, 12, 20, 28, 40, 52, 70, 88, ... (Sloane's A014557).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 A014557in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.
- Bourget's Hypothesis
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