Improved lower bound on an Euclidean Ramsey problem

It was previously shown that any two-colour colouring of K(C_n) must contain a monochromatic planar K_4 subgraph for n >= N^, where 6 <= N^ <= N and N is Graham’s number. The bound was later improved to 11 <= N^* <= N. In this article, it is improved to 13 <= N^* <= N.