Given five points, one can color the edges between the vertices with two colors so that no three vertices are connected with the same color (a monochromatic triangle).

It is well known that if one colors all of the edges between six vertices, then at least one monochromatic triangle results.

What is the minimum number of monochromatic triangles that result from two coloring all of the edges between six vertices? seven? eight? nine?

Can you find a formula for the minimum number of monochromatic triangles that
result from two coloring all of the edges between *n* vertices?

**
The solution will be posted shortly.
**

Back to the Archives

Back to the Math Department Homepage.