For given simple graphs \(H_1,H_2,\ldots ,H_t\), the Ramsey number \(R(H_1,H_2,\ldots ,H_t)\), which is often called multi-color Ramsey number, is the smallest integer n such that for an arbitrary decomposition \(\{G_i\}_{i=1}^t\) of the complete graph \(K_n\), there is at least one \(G_i\) has a subgraph isomorphic to \(H_i\). Let \(m,n_1,n_2,\ldots , n_t\) be positive integers and \(\Sigma =\sum _{i=1}^t(n_i-1)\). Raeisi and Zaghian obtained the \(R(K_{1,n_1},\ldots ,K_{1,n_t},C_m)\) and \(R(K_{1,n_1},\ldots ,K_{1,n_t},W_m)\) for odd \(m\le \Sigma +2\). In this paper, we establish \(R(K_{1,n_1},\ldots ,K_{1,n_t},W_m)\) for odd \(m\ge \Sigma +3\) and even \(m\ge 2\Sigma +2\). We also determine the rest values of \(R(K_{1,n_1},\ldots ,K_{1,n_t},C_m)\) except for even \(m\le \Sigma +1\) and \(R(K_{1,n_1},\ldots ,K_{1,n_t},P_m)\) for \(m\ge \Sigma +1\), or \(m\le \Sigma \) and \(\Sigma \equiv 0,1(\text{ mod }\, m-1)\), which extends a result on \(R(K_{1,n_1},\ldots ,K_{1,n_t},P_m)\) obtained by K. Zhang and S. Zhang.

对于给定的简单图形\（H_1，H_2，\ ldots，H_t \），通常称为多色Ramsey数的Ramsey数\（R（H_1，H_2，\ ldots，H_t）\）是最小的整数n使得对于完整图\（K_n \）的任意分解\（\ {G_i \} _ {i = 1} ^ t \），至少有一个\（G_i \）具有与\同构的子图（H_i \）。假设\（m，n_1，n_2，\ ldots，n_t \）是正整数，并且\（\ Sigma = \ sum _ {i = 1} ^ t（n_i-1）\）。Raeisi和Zaghian获得了\（R（K_ {1，n_1}，\ ldots，K_ {1，n_t}，C_m）\）和\（R（K_ {1，n_1}，\ ldots，K_ {1，n_t }，W_m）\）为奇数\（m \ le \ Sigma +2 \）。在本文中，我们为奇数\（m \ ge \ Sigma +3 \）和偶数\（m \ m建立\（R（K_ {1，n_1}，\ ldots，K_ {1，n_t}，W_m）\）ge 2 \ Sigma +2 \）。我们还确定了\（R（K_ {1，n_1}，\ ldots，K_ {1，n_t}，C_m）\）的其余值，除了\（m \ le \ Sigma +1 \）和\（R （K_ {1，n_1}，\ ldots，K_ {1，n_t}，P_m）\）表示\（m \ ge \ Sigma +1 \）或\（m \ le \ Sigma \）和\（\ Sigma \ equiv 0,1（\ text {mod} \，m-1）\），其结果扩展到\（R（K_ {1，n_1}，\ ldots，K_ {1，n_t}，P_m）\）由K. Zhang和S. Zhang获得。