A generalization of Ramsey theory to mathematical objects in which one would not normally expect structure to be found. For example, there exists a graph with very few triangles (more precisely, a graph which can always be constructed so that there is no "cycle" of triangles which are all distinct and meets in at least one vertex) and such that however it is colored with colors, one of the colors contains a triangle. The usual proof of Ramsey's theorem gives no insight on how to prove such a result.

# Structural Ramsey Theory

## See also

Extremal Graph Theory, Ramsey's Theorem, Ramsey Theory## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Structural Ramsey Theory."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/StructuralRamseyTheory.html