All Complete Graph-Wheel Planar Ramsey Numbers

For two given graphs G_1 and G_2 , the planar Ramsey number PR(G_1,G_2) is the smallest integer N such that for any planar graph G of order N , either G contains G_1 or the complement of G contains G_2 . Let K_m denote a complete graph of order m and W_n a wheel of order n+1 . In this paper, we determine all planar Ramsey numbers PR(K_m,W_n) .