Editing Graph coloring (section)

=== Ramsey theory ===

{{Main|Ramsey theory}}

An important class of ''improper'' coloring problems is studied in [[Ramsey theory]], where the graph's edges are assigned to colors, and there is no restriction on the colors of incident edges. A simple example is the [[theorem on friends and strangers]], which states that in any coloring of the edges of <math>K_6</math>, the complete graph of six vertices, there will be a monochromatic triangle; often illustrated by saying that any group of six people either has three mutual strangers or three mutual acquaintances. Ramsey theory is concerned with generalisations of this idea to seek regularity amid disorder, finding general conditions for the existence of monochromatic subgraphs with given structure.