---
tag: PZD28KZ7YJ
kind: statement
role: proposition
name: Goodman's theorem
sources:
  - wikipedia: en:84088511@r1371858234
    locator: Goodman's theorem
    note: adopted
    mention: wikipedia://en/84088511
    sections: [Statement]
same_as:
  wikidata: Q141446824
  wikipedia: Goodman's theorem
inventory: [5RSRYCM71R]
---

## 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|03WKB2H474]]. 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**.