Hopcroft and Tarjan found over 30 years ago a linear-time test that is
able to test graphs on being 3-connected. This
algorithm is complex and difficult to implement correctly, and even
though some new tests were developed over the time there has not been
much progress in simplifying it, nor on extending it to give an
easy-to-ceck certificate along with its answer to justify it. We propose a new, simple test on the 3-connectedness of graphs that is based on a inductive construction and - in addition - constructs a certificate for the graphs that are 3-connected. The running time is O(n^2), the certificate has linear size and can be verified in linear time as well.