Detecting specific structures in a network has been a very active theme of research in distributed computing for at least a decade. In this paper, we start the study of subgraph detection from the perspective of local certification. Remember that a local certification is a distributed mechanism enabling the nodes of a network to check the correctness of the current configuration, thanks to small pieces of information called certificates. Our main question is: For a given graph $H$, what is the minimum certificate size that allows checking that the network does not contain $H$ as a (possibly induced) subgraph? We show a variety of lower and upper bounds, uncovering an interesting interplay between the optimal certificate size, the size of the forbidden subgraph, and the locality of the verification. Along the way we introduce several new technical tools, in particular what we call the \emph{layered map}, which is not specific to forbidden subgraphs and that we expect to be useful for certifying many other properties.

翻译：网络中的特定结构检测在分布式计算领域已成为至少十年来的研究热点。本文从局部认证的视角开启了子图检测的研究。需知局部认证是一种分布式机制，通过称为证书的小型信息片段，使网络节点能够验证当前配置的正确性。我们的核心问题是：对于给定图$H$，要验证网络不包含$H$作为（可能诱导的）子图，所需的最小证书尺寸是多少？我们展示了一系列下界与上界结果，揭示了最优证书尺寸、禁止子图规模与验证局部性之间有趣的相互作用。在研究过程中，我们引入了若干新技术工具，特别是称为\emph{分层映射}的构造——该工具不仅限于禁止子图认证，我们预期其能用于验证更多其他性质。