  A connected graph is 4-connected if it contains at least five vertices and
removing any three of them does not disconnect it. A frequent preprocessing
step in graph drawing is to decompose a plane graph into its 4-connected
components and to determine their nesting structure. A linear-time algorithm
for this problem was already proposed by Kant. However, using common graph data
structures, we found the subroutine dealing with triangulated graphs difficult
to implement in such a way that it actually runs in linear time. As a drop-in
replacement, we provide a different, easy-to-implement linear-time algorithm
that decomposes a triangulated graph into its 4-connected components and
computes the respective nesting structure. The algorithm is based on
depth-first search.
