This paper introduces sketching based hypothesis tests for some combinatorial properties of Gaussian graphical models. The authors introduce two sketching procedures --- neighborhood sketching and subgraph sketching, and establish that these procedures control FWER, while being computationally efficient. They supplement their theoretical investigations with simulation experiments and carry out a real data analysis. The article attempts to bring together two disparate lines of research--- developments in minimax global testing and multiple testing communities in Statistics on one hand, and Property testing problems in the theoretical computer science literature on the other. I feel this line of research would be of interest to the community, and could lead to interesting future developments.