Certifying 3-Edge-Connectivity

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• 作者：Kurt Mehlhorn ; Adrian Neumann ; Jens M. Schmidt
• 关键词：Certifying algorithm ; Edge connectivity ; Construction sequence
• 刊名：Algorithmica
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：77
• 期：2
• 页码：309-335
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Inform
• 出版者：Springer US
• ISSN：1432-0541
• 卷排序：77

文摘

We present a certifying algorithm that tests graphs for 3-edge-connectivity; the algorithm works in linear time. If the input graph is not 3-edge-connected, the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a construction sequence that constructs the input graph from the graph with two vertices and three parallel edges using only operations that (obviously) preserve 3-edge-connectivity. Additionally, we show how to compute and certify the 3-edge-connected components and a cactus representation of the 2-cuts in linear time. For 3-vertex-connectivity, we show how to compute the 3-vertex-connected components of a 2-connected graph.