Given graphs F, H and G, we say that G is (F, H )_v‐Ramsey if every red/blue vertex coloring of G contains a red copy of F or a blue copy of H. Results of Łuczak, Ruciński and Voigt, and Kreuter determine the threshold for the property that the random graph G(n, p) is (F, H )_v‐Ramsey. In this paper we consider the sister problem in the setting of randomly perturbed graphs. In particular, we determine how many random edges one needs to add to a dense graph to ensure that with high probability the resulting graph is (F, H )_v‐Ramsey for all pairs (F, H) that involve at least one clique.

中文翻译：

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随机摄动图的顶点拉姆齐性质

鉴于图表˚F，  ^ h和摹，我们说摹是（˚F，  ^ h）_v -Ramsey如果每个红色/蓝色顶点来着色摹包含一个红色的副本˚F或蓝色副本^ h。Łuczak，Ruciński和Voigt和Kreuter的结果确定了随机图G（n，  p）为（F，  H）_v -Ramsey的属性的阈值。本文考虑随机扰动图设置中的姐妹问题。特别是，我们确定需要向密集图中添加多少个随机边，以确保对于涉及至少一个集团的所有对（F，  H），结果图极有可能是（F，  H）_v- Ramsey 。