We develop a method to study sufficient conditions for perfect mixed tilings. Our framework allows the embedding of bounded degree graphs H with components of sublinear order. As a corollary, we recover and extend the work of Kühn and Osthus regarding sufficient minimum degree conditions for perfect F-tilings (for an arbitrary fixed graph F) by replacing the F-tiling with the aforementioned graphs H. Moreover, we obtain analogous results for degree sequences and in the setting of uniformly dense graphs. Finally, we asymptotically resolve a conjecture of Komlós in a strong sense.

中文翻译：

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完美的混合瓷砖的充足条件


我们开发了一种方法来研究完美混合平铺的充分条件。我们的框架允许将有界度图 H 嵌入到次线性阶的分量中。作为推论，我们恢复并扩展了 Kühn 和 Osthus 关于完美 F 平铺（对于任意固定图 F）的足够最小度条件的工作，方法是将 F 平铺替换为上述图 H。此外，我们获得了度数序列和均匀密集图设置的类似结果。最后，我们从强意义上渐近地解决了 Komlós 的猜想。