• clique
• maximal subgraph
• reverse search
• set system
• temporal network

The problem of listing subgraphs that satisfy a certain property represents, in many cases, a hard problem. Despite its inner difficulty, driven by the many applications, a lot of algorithms have been studied to optimize the computational and memory cost that is needed to solve this kind of problems. In this work we focus on listing subgraphs that satisfy a certain property and are maximal under inclusion. A successful general formalism to work with these kind of problems is using set systems, since they can model many interesting properties such as cliques, cuts, k-plexes and others.
First we present a general framework, that through the technique of reverse search, consists in a powerful tool for enumerating maximal solutions. Then we present a model of temporal network and apply the more general framework to the specific problem of finding maximal cliques in temporal graphs.