A graph is called cyclically 4-edge-connected if removing any three edges from it results in a graph in which at most one connected component contains a cycle. A 3-connected graph is 4-edge-connected if and only if removing any three edges from it results in either a connected graph or a graph with exactly two connected components one of which is a single-vertex one. We show how to associate with any 3-connected graph a tree of components such that every component is a 3-connected and cyclically 4-edge-connected graph.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 450, 2016, pp. 109–150.
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Pastor, A.V. On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components. J Math Sci 232, 61–83 (2018). https://doi.org/10.1007/s10958-018-3859-0
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DOI: https://doi.org/10.1007/s10958-018-3859-0