The graph removal lemma is a fundamental result in extremal graph theory which says that for every fixed graph H and $\epsilon >0$, if an n-vertex graph G contains $\epsilon n^2$ edge-disjoint copies of H then G contains $\delta n^{v(H)}$ copies of H for some $\delta =\delta (\epsilon ,H)>0$. The current proofs of the removal lemma give only very weak bounds on $\delta (\epsilon ,H)$, and it is also known that $\delta (\epsilon ,H)$ is not polynomial in ε unless H is bipartite. Recently, Fox and Wigderson initiated the study of minimum degree conditions guaranteeing that $\delta (\epsilon ,H)$ depends polynomially or linearly on ε. In this paper we answer several questions of Fox and Wigderson on this topic.

中文翻译：

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最小程度移除引理阈值

图移除引理是极值图论的基本结果，它表示对于每个固定图H和$\epsilon >0$，如果一个n顶点图G包含$\epsilon n^2$H的边不相交副本，然后G包含$\delta n^{v（H）}$某些人的H副本$\delta =\delta （\epsilon ,H）>0$。当前移除引理的证明仅给出了非常弱的界限$\delta （\epsilon ,H）$，并且还已知$\delta （\epsilon ,H）$除非H是二部的，否则不是ε中的多项式。最近，Fox 和 Wigderson 发起了最低学位条件的研究，以保证$\delta （\epsilon ,H）$多项式或线性取决于ε。在本文中，我们回答了 Fox 和 Wigderson 关于此主题的几个问题。