An edge-colored graph $G$ is rainbow if each edge receives a different color. For a connected graph $H$, $G$ is rainbow $H$-free if $G$ does not contain a rainbow subgraph which is isomorphic to $H$. By definition, if $H^{\prime }$ is a connected subgraph of $H$, every rainbow $H^{\prime }$-free graph is rainbow $H$-free. In this note, we consider a kind of reverse implication, where $H^{\prime }$ is a connected proper supergraph and every rainbow $H^{\prime }$-free graph edge-colored in sufficiently many colors is rainbow $H$-free. We determine when this implication occurs.

中文翻译：

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彩虹禁止子图中的含义

边色图 $G$如果每个边缘接收到不同的颜色，则为彩虹。对于连接图$H$， $G$ 是彩虹 $H$-如果 $G$ 不包含与 $H$。根据定义，如果$H^{\prime }$ 是的连接子图 $H$，每条彩虹 $H^{\prime }$-免费图是彩虹 $H$-自由。在本说明中，我们考虑一种反向含义，其中$H^{\prime }$ 是一个相互联系的适当的上记，每个彩虹 $H^{\prime }$边缘的颜色足够多的自由图是彩虹 $H$-自由。我们确定何时发生这种暗示。