Color edges of K₆ red or blue. By Ramsey's theorem, a monochromatic triangle is unavoidable!
Red triangles: 0
Blue triangles: 0
Uncolored edges: 15
Select a color, then click edges to color them.
Ramsey number R(3,3)=6: In any 2-coloring of the edges of K₆ (complete graph on 6 vertices), there must exist
at least one monochromatic triangle. This is tight: K₅ can be 2-colored without any monochromatic triangle.
Proof sketch: Fix vertex v. It has 5 edges; by pigeonhole ≥3 are the same color (say red). Among those 3 neighbors,
if any connecting edge is red → red triangle; if all 3 edges are blue → blue triangle.