Problem
COM-B2-M06-P004 A Pentagon Without a Monochromatic Triangle
#4
★★☆☆☆ Level 2 of 5
Construct a red-blue colouring of the edges of \(K_5\) with no monochromatic triangle.
Place the vertices on a circle: colour sides and diagonals differently.
Place the vertices as a pentagon. Colour the five sides red and the five diagonals blue.
The red graph is a cycle of length \(5\), so there is no red triangle. The blue graph is also a cycle of length \(5\), so there is no blue triangle.
Lower bound for \(R(3,3)\): five vertices are not enough.