The planar Ramsey number PR(C4,K8)PR(C4,K8)

For two given graphs G1G1 and G2G2, the planar Ramsey number PR(G1,G2)PR(G1,G2) is the smallest integer NN such that for any planar graph GG on NN vertices, either GG contains G1G1 or its complement contains G2G2. Let CnCn denote a cycle of length nn and KlKl a complete graph of order ll. Sun, Yang, Lin and Song conjectured that PR(C4,Kl)=3l+⌊(l−1)/5⌋−2PR(C4,Kl)=3l+⌊(l−1)/5⌋−2 and the conjecture was proved for l≤7l≤7. In this paper, it is shown that PR(C4,K8)=23PR(C4,K8)=23 which confirms the conjecture for l=8l=8.