We prove a rainbow version of the blow‐up lemma of Komlós, Sárközy, and Szemerédi for μn‐bounded edge colorings. This enables the systematic study of rainbow embeddings of bounded degree spanning subgraphs. As one application, we show how our blow‐up lemma can be used to transfer the bandwidth theorem of Böttcher, Schacht, and Taraz to the rainbow setting. It can also be employed as a tool beyond the setting of μn‐bounded edge colorings. Kim, Kühn, Kupavskii, and Osthus exploit this to prove several rainbow decomposition results. Our proof methods include the strategy of an alternative proof of the blow‐up lemma given by Rödl and Ruciński, the switching method, and the partial resampling algorithm developed by Harris and Srinivasan.

中文翻译：

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彩虹爆炸引理

我们证明Komlós，萨科齐和Szemerédi为吹胀引理的彩虹版微牛-bounded边缘色素。这使得系统地研究有界度跨越子图的彩虹嵌入。作为一个应用程序，我们展示了如何使用爆炸引理将Böttcher，Schacht和Taraz的带宽定理转换为彩虹设置。它也可以被用作超出的设定的工具μN -bounded边着色。Kim，Kühn，Kupavskii和Osthus利用这一点证明了几个彩虹分解结果。我们的证明方法包括Rödl和Ruciński给出的爆破引理的替代证明策略，切换方法以及Harris和Srinivasan开发的部分重采样算法。