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Computing the 4-Edge-Connected Components of a Graph in Linear Time

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Abstract

We present the first linear-time algorithm that computes the 4-edge-connected components of an undirected graph. Hence, we also obtain the first linear-time algorithm for testing 4-edge connectivity. Our results are based on a linear-time algorithm that computes the 3-edge cuts of a 3-edge-connected graph G, and a linear-time procedure that, given the collection of all 3-edge cuts, partitions the vertices of G into the 4-edge-connected components.
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hal-03474050 , version 1 (10-12-2021)

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Loukas Georgiadis, Giuseppe F Italiano, Evangelos Kosinas. Computing the 4-Edge-Connected Components of a Graph in Linear Time. ESA 2021 - 29th Annual European Symposium on Algorithms, Sep 2021, Lisbon, Portugal. pp.1-41. ⟨hal-03474050⟩

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