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.
- Fibonacci Pseudoprime
- Fibonacci Q-Matrix
- Fibonacci Sequence
- Fibration
- Field
- Field Axioms
- Field Extension
- Fields Medal
- Fifteen Theorem
- Figurate Number
- Figurate Number Triangle
- Figure Eight Knot
- Figure Eight Surface
- Figure-of-Eight Knot
- Figures
- Filon's Integration Formula
- Filter
- Fine's Equation
- Finite
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- Finite Group D3
- Finite Group D4