Removable edges of a spanning tree in 3-connected 3-regular graphs

Authors:
Haiyan Kang;Jichang Wu;Guojun Li
Affiliations:
School of Mathematics and System Sciences, Shandong University, Jinan, China;School of Mathematics and System Sciences, Shandong University, Jinan, China;School of Mathematics and System Sciences, Shandong University, Jinan, China and CSBL, Department of Biochemistry and Molecular, Biology Institute of Bioinformatics, University of Georgia, GA
Venue:
FAW'07 Proceedings of the 1st annual international conference on Frontiers in algorithmics
Year:
2007

Citing 4
Cited 1

Removable edges in 3-connected graphs

Journal of Graph Theory
The number of removable edges in 3-connected graphs

Journal of Combinatorial Theory Series B
Graph Theory With Applications

Graph Theory With Applications
Using expander graphs to find vertex connectivity

Journal of the ACM (JACM)

Every DFS Tree of a 3-Connected Graph Contains a Contractible Edge

Journal of Graph Theory

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Abstract

Let G be a 3-connected graph and e an edge of G. If, by deleting e from G, the resultant graph G-e is a 3-connected graph or a subdivision of a 3-connected graph, then e is called a removable edge of G. In this paper we obtain that there are at least two removable edges in a spanning tree of a 3-connected 3-regular graph. Also we give an O(n3) time algorithm to find all removable edges in G.