An infinite graph is highly connected if the complement of any subgraph of smaller size is connected. We consider weaker versions of Ramsey’s Theorem asserting that in any coloring of the edges of a complete graph there exist large highly connected subgraphs all of whose edges are colored by the same color.

中文翻译：

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高度连通单色子图的拉姆齐理论

如果任何较小尺寸的子图的补是连通的，则无限图是高度连通的。我们考虑拉姆齐定理的较弱版本，该定理断言在完整图的边的任何着色中，都存在大的高度连接的子图，所有子图的边都用相同的颜色着色。