We introduce a counterpart to the notion of tilings, that is vertex-disjoint copies of a fixed graph $F$, to the setting of graphons. The case $F=K_2$ gives the notion of matchings in graphons. We give a transference statement that allows us to switch between the finite and limit notion, and derive several favorable properties, including the LP-duality counterpart to the classical relation between the fractional vertex covers and fractional matchings/tilings, and discuss connections with property testing.

As an application of our theory, we determine the asymptotically almost sure $F$-tiling number of inhomogeneous random graphs $\mathbb{G}(n,W)$. As another application, in an accompanying paper (Hladký et al., 2019) we give a proof of a strengthening of a theorem of Komlós (Komlós, 2000).

我们介绍了平铺的概念，即固定图的顶点不相交的副本 $F$，以设置Graphon。案子$F={ķ}_2$给出了石墨烯中匹配的概念。我们给出一个转移语句，使我们可以在有限和极限概念之间切换，并得出几个有利的属性，包括与分数顶点覆盖和分数匹配/平铺之间的经典关系对应的LP对偶，并讨论与属性测试的关系。

作为我们理论的应用，我们确定渐近几乎确定 $F$不均匀随机图的平铺数目 $\mathbb{G}（ñ，\mathrm{w\; ^}）$。作为另一项应用，在随附的论文中（Hladký等，2019），我们证明了Komlós定理的增强（Komlós，2000）。