Goodman's theorem

Statement

In graph theory, Goodman's theorem gives the exact minimum number of monochromatic triangles in a two-coloring of the edges of a complete graph. If the edges of $K_n$ are colored red or blue, the minimum depends on $n$ modulo four. A. W. Goodman published the result in 1959, phrasing the two colors as pairs of acquaintances and strangers at a party. Forms of the result are also known as Goodman's formula.