b'@online{Kurt3edge2013,'b'\nTITLE = {Certifying 3-Edge-Connectivity},\nAUTHOR = {Mehlhorn, Kurt and Neumann, Adrian and Schmidt, Jens M.},\nLANGUAGE = {eng},\nURL = {http://arxiv.org/abs/1211.6553},\nEPRINT = {1211.6553},\nEPRINTTYPE = {arXiv},\nYEAR = {2013},\nABSTRACT = {We present a certifying algorithm that tests graphs for 3-edge-connectivity; the algorithm works in linear time. If the input graph is not 3-edge-connected, the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a construction sequence that constructs the input graph from the graph with two vertices and three parallel edges using only operations that (obviously) preserve 3-edge-connectivity. Additionally, we show how compute and certify the 3-edge-connected components and a cactus representation of the 2-cuts in linear time. For 3-vertex-connectivity, we show how to compute the 3-vertex-connected components of a 2-connected graph.},\n}\n'