A subgraph of an edge-coloured graph is called rainbow if all its edges have different colours. We prove a rainbow version of the blow-up lemma of Komlós, Sárközy, and Szemerédi that applies to almost optimally bounded colourings. A corollary of this is that there exists a rainbow copy of any bounded-degree spanning subgraph H in a quasirandom host graph G, assuming that the edge-colouring of G fulfills a boundedness condition that is asymptotically best possible. This has many applications beyond rainbow colourings: for example, to graph decompositions, orthogonal double covers, and graph labellings.

中文翻译：

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几乎最优有界边缘着色的彩虹膨胀引理

有色图的子图称为彩虹如果它的所有边缘都有不同的颜色。我们证明了 Komlós、Sárközy 和 Szemerédi 的爆炸引理的彩虹版本，它适用于几乎最优的有界着色。一个推论是存在任何有界度跨越子图的彩虹副本H在准随机主机图中G，假设边缘着色G满足渐近最佳可能的有界条件。除了彩虹着色之外，它还有许多应用：例如，用于图形分解、正交双覆盖和图形标签。