R(C6, K5) = 21andR(C7, K5) = 25

R(C4, K4) = 10 (see [2]) R(C4, K5) = 14 (see [3]) R(C5, K4) = 13, R(C5, K5) = 17 (see [5, 6]) R(Cn, K3) = 2n − 1 (n > 3) (see [4, 7]). In [10], we proved that R(Cn, K4) = 3(n − 1) + 1 (n ≥ 4). In this paper, we will prove that R(Cn, K5) = 4(n − 1)+ 1 (n = 6, 7). The following notations will be used in this paper. If G is a graph, the vertex set (resp. edge set) of G is denoted by V (G) (resp. E(G)). For x ∈ V (G), N (x) = {v ∈ V (G)|xv ∈ E(G)}. If V ⊂ V (G), then N (V ) = ⋃ x∈V N (x). A cycle with n vertices x1, x2, . . . , xn will be denoted by