A rainbow blow-up lemma - Glock, Stefan; Joos, Felix (Random structures & algorithms, 2020)
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.