We consider countable edge colourings of complete graphs and investigate the existence of monochromatic paths. We show how this depends on the sizes of the complete graphs whose edges are being coloured.

中文翻译：

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路径的 Erdős–Kakutani 现象

我们考虑完整图的可数边缘着色并研究单色路径的存在。我们展示了这如何取决于边缘被着色的完整图的大小。