Schwenk's Formula

Let R+B be the number of monochromatic forced triangles (where R and B are the number of red and blue triangles) in an extremal graph. Then

 R+B=(n; 3)-|_1/2n|_1/4(n-1)^2_|_|,

where (n; k) is a binomial coefficient and |_x_| is the floor function (Schwenk 1972).

See also

Extremal Graph, Monochromatic Forced Triangle

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Schwenk, A. J. "Acquaintance Party Problem." Amer. Math. Monthly 79, 1113-1117, 1972.

Referenced on Wolfram|Alpha

Schwenk's Formula

Cite this as:

Weisstein, Eric W. "Schwenk's Formula." From MathWorld--A Wolfram Web Resource.

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