基于图子覆盖的Komlós平铺定理
Komlós's tiling theorem via graphon covers
摘要：
科姆洛斯[科姆洛斯：Tiling Turan Theorms，Combinatorica，2000]确定了一个固定图H的顶点不相交副本覆盖宿主图的给定比例的顶点的渐近最优最小度条件，从而本质上扩展了Hajnal-Szemeredi定理，该定理处理H是团的情况。我们给出了一个证明的graphon版本的Komlos定理。为了证明这个graphon版本，并从它推导出关于有限图的原始陈述，我们使用[Hladky，Hu，Piguet：Tilings in graphons，arXiv：1606.03113]中介绍的机器。我们进一步证明了Komlos定理的一个稳定性版本。
英文摘要：
Komlos [Komlos: Tiling Turan Theorems, Combinatorica, 2000] determined the asymptotically optimal minimum-degree condition for covering a given proportion of vertices of a host graph by vertex-disjoint copies of a fixed graph H, thus essentially extending the Hajnal-Szemeredi theorem which deals with the case when H is a clique. We give a proof of a graphon version of Komlos's theorem. To prove this graphon version, and also to deduce from it the original statement about finite graphs, we use the machinery introduced in [Hladky, Hu, Piguet: Tilings in graphons, arXiv:1606.03113]. We further prove a stability version of Komlos's theorem.
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