Theorem on Friends and Strangers

The theorem on friends and strangers, a result in Ramsey theory distinct from the unrelated friendship theorem of Paul Erdos, Alfred Renyi and Vera Sos, states that among any six people, there must be either three who are mutual acquaintances or three who are mutual strangers. The proof represents the six people as the vertices of a complete graph on six vertices with each edge colored red for strangers or blue for acquaintances, and shows that no matter how the graph's fifteen edges are colored with the two colors, a monochromatic triangle, either all red or all blue, always appears. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/