For given r-uniform hypergraphs \({\mathcal {G}}\) and \({\mathcal {H}}\), the Ramsey number \(R({\mathcal {G}},{\mathcal {H}};r)\) is defined as the smallest positive integer p such that any red/blue coloring of the edges of the complete r-uniform hypergraph on p vertices contains either a red copy of \({\mathcal {G}}\) or a blue copy of \({\mathcal {H}}\). The hypergraph \({\mathcal {G}}\) is called \({\mathcal {H}}\)-good, if \(R({\mathcal {G}},{\mathcal {H}};r)=(|V({\mathcal {G}})|-1) (\chi ({\mathcal {H}})-1)+s({\mathcal {H}}),\) where \(s({\mathcal {H}})\) is the chromatic surplus number of \({\mathcal {H}}\), i.e., the minimum cardinality of color classes over all colorings of \(V({\mathcal {H}})\) with \(\chi ({\mathcal {H}})\) colors. In this note, for a given r-uniform hypergraph \({\mathcal {H}}\), the exact value of the Ramsey number of the disjoint union of \({\mathcal {H}}\)-good hypergraphs versus \({\mathcal {H}}\) will be determined exactly.

对于给定的r一致超图\（{\ mathcal {G}} \）和\ {{\ mathcal {H}} \}，拉姆西数\（R（{\ mathcal {G}}，{\ mathcal {H }}; r）\）定义为最小的正整数p，以使p个顶点上完整r-一致超图的边缘的任何红色/蓝色着色都包含\（{\ mathcal {G}}的红色副本\）或\（{\ mathcal {H}} \）的蓝色副本。超图\（{\ mathcal {G}} \）称为\（{\ mathcal {H}} \}-好，如果\（R（{\ mathcal {G}}，{\ mathcal {H}}; r）=（| V（{\ mathcal {G}}）| -1）（\ chi（{\ mathcal {H}}）-1）+ s（{\ mathcal {H}}），\）其中\（s（{{mathcal {H}}）\）是\（{\ mathcal {H}} \）的色余数，即\（V（{ \ mathcal {H}}）\）具有\（\ chi（{\ mathcal {H}}）\）颜色。在本说明，对于给定的[R -uniform超图\（{\ mathcal {H}} \） ，的不相交并的Ramsey数的精确值\（{\ mathcal {H}} \） -良好对比超图\（{\ mathcal {H}} \）将被完全确定。