Heinrich, I.I.HeinrichHeller, T.T.HellerSchmidt, E.E.SchmidtStreicher, M.M.Streicher2022-03-142022-03-142020https://publica.fraunhofer.de/handle/publica/40976810.1007/978-3-030-60440-0_282-s2.0-85093821483If a biconnected graph stays connected after the removal of an arbitrary vertex and an arbitrary edge, then it is called 2.5-connected. We prove that every biconnected graph has a canonical decomposition into 2.5-connected components. These components are arranged in a tree-structure. We also discuss the connection between 2.5-connected components and triconnected components and use this to present a linear time algorithm which computes the 2.5-connected components of a graph. We show that every critical 2.5-connected graph other than K4 can be obtained from critical 2.5-connected graphs of smaller order using simple graph operations. Furthermore, we demonstrate applications of 2.5-connected components in the context of cycle decompositions and cycle packings.en003006519conference paper