Let r(G₁, G₂) be the Ramsey number of the two graphs G₁ and G₂. For n₁ ⩾ n₂ ⩾ 1 let S(n₁, n₂) be the double star given by \(V\left( {S\left( {{n_1},{n_2}} \right)} \right) = \left\{ {{v_0},{v_1}, \ldots ,{v_{{n_1}}},{w_0},{w_1}, \ldots ,{w_{{n_2}}}} \right\}\) and \(E\left( {S\left( {{n_1},{n_2}} \right)} \right) = \left\{ {{v_0}{v_1}, \ldots ,{v_0}{v_{{n_1}}},{v_0}{w_0},{w_0}{w_1}, \ldots ,{w_0}{w_{{n_2}}}} \right\}\). We determine r(K_1,m−1, S(n₁, n₂)) under certain conditions. For n ⩾ 6 let \(T_n^3 = S(n - 5,3),T_n^{\prime\prime} = (V,{E_2})\) and \(T_n^{\prime\prime\prime} = (V,{E_3})\), where \(V = \left\{ {{v_0},{v_1}, \ldots ,{v_{n - 1}}} \right\},\;{E_2} = \left\{ {{v_0}{v_1}, \ldots ,{v_0}{v_{n - 4}},{v_1}{v_{n - 3}},{v_1}{v_{n - 2}},{v_2}{v_{n - 1}}} \right\}\) and \({E_3} = \left\{ {{v_0}{v_1}, \ldots ,{v_0}{v_{n - 4}},{v_1}{v_{n - 3}},{v_2}{v_{n - 2}},{v_3}{v_{n - 1}}} \right\}\). We also obtain explicit formulas for \(r({K_{1,m - 1}},{T_n}),\;r(T_m^\prime,{T_n})\;(n \geqslant m + 3),\;r({T_n},{T_n}),\;r(T_n^\prime,{T_n})\) and r(P_n, T_n), where \({T_n} \in \left\{ {T_n^{\prime\prime},T_n^{\prime\prime\prime},T_n^3} \right\}\), P_n is the path on n vertices and \(T_n^\prime\) is the unique tree with n vertices and maximal degree n − 2.

令r（G ₁，G ₂）为两个图G ₁和G ₂的Ramsey数。对于Ñ ₁ ⩾ Ñ ₂ ⩾1让小号（Ñ ₁，Ñ ₂）是由下式给出的双星\（V \左（{S \左（{{N_1}，{N_2}} \右）} \右） = \ left \ {{{v_0}，{v_1}，\ ldots，{v _ {{n_1}}}，{w_0}，{w_1}，\ ldots，{w _ {{n_2}}}} \ right \} \）和\（E \ left（{S \ left（{{n_1}，{n_2}} \ right）} \ right）= \ left \ {{{v_0} {v_1}，\ ldots，{v_0} { v _ {{n_1}}，{v_0} {w_0}，{w_0} {w_1}，\ ldots，{w_0} {w _ {{n_2}}}} \ right \} \）。我们在特定条件下确定r（K _{1，m -1}，S（n ₁，n ₂））。对于Ñ ⩾6令\（T_n ^ 3 = S（N - 5,3），T_n ^ {\素\素} =（V，{E_2}）\）和\（T_n ^ {\素\素\素} =（V，{E_3}）\），其中\（V = \ left \ {{{v_0}，{v_1}，\ ldots，{v_ {n-1}}}} \ right \}，\; { E_2} = \ left \ {{{v_0} {v_1}，\ ldots，{v_0} {v_ {n-4}}，{v_1} {v_ {n-3}}，{v_1} {v_ {n- 2}}，{v_2} {v_ {n-1}}} \ right \} \）和\（{E_3} = \ left \ {{{v_0} {v_1}，\ ldots，{v_0} {v_ { n-4}}，{v_1} {v_ {n-3}}，{v_2} {v_ {n-2}}，{v_3} {v_ {n-1}}} \ right \} \）。我们还获得了以下公式的显式\（r（{K_ {1，m-1}}，{T_n}），\; r（T_m ^ \ prime，{T_n}）\;（n \ geqslant m + 3），\; r（{T_n }，{T_n}），\; r（T_n ^ \ prime，{T_n}）\）和r（P _n，T _n），其中\（{T_n} \ in \ left \ {{T_n ^ {\ prime \ prime}，T_n ^ {\ prime \ prime \ prime}，T_n ^ 3} \ right \} \），P _n是n个顶点上的路径，\（T_n ^ \ prime \）是具有n个顶点的唯一树和最大度数n − 2