Certifying 3-edge-connectivity

Publikationstyp
Journal Article
Date Issued
2017
Sprache
English
Author(s)
Mehlhorn, Kurt  
Neumann, Adrian  
Schmidt, Jens M.  orcid-logo
TORE-URI
http://hdl.handle.net/11420/7607
Journal
Algorithmica  
Volume
77
Issue
2
Start Page
309
End Page
335
Citation
Algorithmica (2017)
Publisher DOI
10.1007/s00453-015-0075-x
Scopus ID
2-s2.0-84944550603
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.
Subjects
Certifying algorithm
Construction sequence
Edge connectivity
DDC Class
510: Mathematik