2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173634It 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.8 pages, 1 figureCombinatoricstext