Schmidt, Jens M.Jens M.Schmidt2020-10-192020-10-192012Algorithmica (2012)http://hdl.handle.net/11420/7591Tutte proved that every 3-vertex-connected graph G on more than 4 vertices has a contractible edge. Barnette and Grünbaum proved the existence of a removable edge in the same setting. We show that the sequence of contractions and the sequence of removals from G to K₄ can be computed in O(|V|²) time by extending Barnette's and Grünbaum's theorem. As an application, we derive a certificate for the 3-vertex-connectivity of graphs that can be easily computed and verified.en1432-05412012192208SpringerMathematikJournal Article10.1007/s00453-010-9450-9Journal Article