Determining 4-edge-connected components in linear time
Wojciech Nadara, Mateusz Radecki, Marcin Smulewicz, Marek, Soko{\l}owski
TL;DR
This paper introduces the first deterministic linear-time algorithm for identifying 4-edge-connected components in undirected graphs, utilizing a novel approach to list all 3-edge-cuts in 3-edge-connected graphs.
Contribution
It presents a new linear-time deterministic algorithm for computing 4-edge-connected components, including an algorithm for listing all 3-edge-cuts in 3-edge-connected graphs.
Findings
First linear-time deterministic algorithm for 4-edge-connected components
Algorithm efficiently lists all 3-edge-cuts in 3-edge-connected graphs
Enables faster analysis of graph connectivity structures
Abstract
In this work, we present the first linear time deterministic algorithm computing the 4-edge-connected components of an undirected graph. First, we show an algorithm listing all 3-edge-cuts in a given 3-edge-connected graph, and then we use the output of this algorithm in order to determine the 4-edge-connected components of the graph.
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