The planar Ramsey number for C4 and K5 is 13 Original Research Article

The planar Ramsey number PR(G,H) is the smallest integer n such that in any two-colouring (red and blue) of edges of Kn such that the red colour induces a planar graph there is a red subgraph G or a blue subgraph H. It is known that Ramsey number for C4 and K5 equals to 14. In this paper we show that PR(C4,K5)=13.