  The girth of a graph is the length of its shortest cycle. Due to its
relevance in graph theory, network analysis and practical fields such as
distributed computing, girth-related problems have been object of attention in
both past and recent literature. In this paper, we consider the problem of
listing connected subgraphs with bounded girth. As a large girth is index of
sparsity, this allows to extract sparse structures from the input graph. We
propose two algorithms, for enumerating respectively vertex induced subgraphs
and edge induced subgraphs with bounded girth, both running in $O(n)$ amortized
time per solution and using $O(n^3)$ space. Furthermore, the algorithms can be
easily adapted to relax the connectivity requirement and to deal with weighted
graphs. As a byproduct, the second algorithm can be used to answer the well
known question of finding the densest $n$-vertex graph(s) of girth $k$.
