  In this paper, we study the information theoretic bounds for exact recovery
in sub-hypergraph models for community detection. We define a general model
called the $m-$uniform sub-hypergraph stochastic block model ($m-$ShSBM). Under
the $m-$ShSBM, we use Fano's inequality to identify the region of model
parameters where any algorithm fails to exactly recover the planted communities
with a large probability. We also identify the region where a Maximum
Likelihood Estimation (MLE) algorithm succeeds to exactly recover the
communities with high probability. Our bounds are tight and pertain to the
community detection problems in various models such as the planted hypergraph
stochastic block model, the planted densest sub-hypergraph model, and the
planted multipartite hypergraph model.
