A simple certifying algorithm for 3-edge-connectivity

TL;DR

This paper introduces a linear-time certifying algorithm for determining 3-edge-connectivity in graphs, efficiently providing certificates or decompositions with a single pass, applicable even to graphs that are not 2-edge-connected.

Contribution

It presents a novel, efficient certifying algorithm for 3-edge-connectivity that works in linear time and handles graphs not necessarily 2-edge-connected.

Findings

Algorithm runs in linear time

Generates certificates or decompositions

Works on graphs not necessarily 2-edge-connected

Abstract

A linear-time certifying algorithm for 3-edge-connectivity is presented. Given an undirected graph G, if G is 3-edge-connected, the algorithm generates a construction sequence as a positive certificate for G. Otherwise, the algorithm decomposes G into its 3-edge-connected components and at the same time generates a construction sequence for each connected component as well as the bridges and a cactus representation of the cut-pairs in G. All of these are done by making only one pass over G using an innovative graph contraction technique. Moreover, the graph need not be 2-edge-connected.