Goodman's Formula
A two-coloring of a Complete Graph 
of 
nodes which contains exactly the number of MonochromaticForced Triangles and no more (i.e., a minimum of 
where 
and 
are the number ofred and blue Triangles) is called an Extremal Graph. Goodman (1959) showed that for an extremalgraph,
 |  |  |
Schwenk (1972) rewrote the equation in the form
where
is a Binomial Coefficient and 
is theFloor Function. 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.
- Small Rhombihexahedron
- Small Snub Icosicosidodecahedron
- Small Stellapentakis Dodecahedron
- Small Stellated Dodecahedron
- Small Stellated Triacontahedron
- Small Stellated Truncated Dodecahedron
- Small Triakis Octahedron
- Small Triambic Icosahedron
- Small World Problem
- Smarandache Ceil Function
- Smarandache Constants
- Smarandache Function
- Smarandache-Kurepa Function
- Smarandache Near-to-Primorial Function
- Smarandache Paradox
- Smarandache Sequences
- Smarandache-Wagstaff Function
- Smith Brothers
- Smith Conjecture
- Smith Normal Form
- Smith Number
- Smith's Markov Process Theorem
- Smith's Network Theorem
- Smooth Manifold
- Smooth Number