  A set of vertices in a graph forms a potential maximal clique if there exists
a minimal chordal completion in which it is a maximal clique. Potential maximal
cliques were first introduced as a key tool to obtain an efficient, though
exponential-time algorithm to compute the treewidth of a graph. As a byproduct,
this allowed to compute the treewidth of various graph classes in polynomial
time.
  In recent years, the concept of potential maximal cliques regained interest
as it proved to be useful for a handful of graph algorithmic problems. In
particular, it turned out to be a key tool to obtain a polynomial time
algorithm for computing maximum weight independent sets in $P_5$-free and
$P_6$-free graphs (Lokshtanov et al., SODA `14 and Grzeskik et al., SODA `19.
In most of their applications, obtaining all the potential maximal cliques
constitutes an algorithmic bottleneck, thus motivating the question of how to
efficiently enumerate all the potential maximal cliques in a graph $G$.
  The state-of-the-art algorithm by Bouchitt\'e \& Todinca can enumerate
potential maximal cliques in output-polynomial time by using exponential space,
a significant limitation for the size of feasible instances. In this paper, we
revisit this algorithm and design an enumeration algorithm that preserves an
output-polynomial time complexity while only requiring polynomial space.
