For a graph G and a family of graphs \(\cal{H}\) , the Ramsey number \(r(G,\cal{H})\) is defined as the minimum integer n such that any red/blue edge-coloring of Kn contains either a red copy of G or a blue copy of some member in \(\cal{H}\) . In this paper, we determine the exact value of \(r(\hat{K}_{n},\cal{L})\) , where \(\hat{K}_{n}\) is a kipas and \(\cal{L}\) is a set of linear forests with a given size. Using the result, we further determine the Gallai-Ramsey number \(\text{gr}_{3}(K_{1,3}:\hat{K}_{n})\) , which is the minimum integer N such that any 3-edge-colored KN contains either a rainbow copy of K1,3 or a monochromatic copy of \(\hat{K}_{n}\) .
