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arXiv · 2105.02910

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

Loukas Georgiadis·Giuseppe F. Italiano·Evangelos Kosinas
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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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Loukas Georgiadis, Giuseppe F. Italiano, Evangelos Kosinas. 2021-05-06. Computing the $4$-Edge-Connected Components of a Graph in Linear Time. https://arxiv.org/abs/2105.02910

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