Kim, Kühn, Osthus and Tyomkyn (Trans. Amer. Math. Soc. 371 (2019), 4655–4742) greatly extended the well-known blow-up lemma of Komlós, Sárközy and Szemerédi by proving a ‘blow-up lemma for approximate decompositions’ which states that multipartite quasirandom graphs can be almost decomposed into any collection of bounded degree graphs with the same multipartite structure and slightly fewer edges. This result has already been used by Joos, Kim, Kühn and Osthus to prove the tree packing conjecture due to Gyárfás and Lehel from 1976 and Ringel’s conjecture from 1963 for bounded degree trees as well as implicitly in the recent resolution of the Oberwolfach problem (asked by Ringel in 1967) by Glock, Joos, Kim, Kühn and Osthus.

Here we present a new and significantly shorter proof of the blow-up lemma for approximate decompositions. In fact, we prove a more general theorem that yields packings with stronger quasirandom properties which is useful for potential applications.

Kim, Kühn, Osthus 和 Tyomkyn (Trans. Amer. Math. Soc. 371 (2019), 4655–4742) 通过证明“近似分解，它指出多部准随机图几乎可以分解为具有相同多部结构和略少边的有界度图的任何集合。这个结果已经被 Joos、Kim、Kühn 和 Osthus 用于证明 1976 年 Gyárfás 和 Lehel 的树堆积猜想和 1963 年 Ringel 的有界度树猜想，以及最近解决 Oberwolfach 问题（被问Ringel 于 1967 年）由 Glock、Joos、Kim、Kühn 和 Osthus 撰写。

在这里，我们提出了一个关于近似分解的爆破引理的新的和明显更短的证明。事实上，我们证明了一个更一般的定理，该定理产生了具有更强拟随机性质的填料，这对潜在的应用很有用。