Chapter

Frontiers in Algorithmics

Volume 4613 of the series Lecture Notes in Computer Science pp 337-345

Removable Edges of a Spanning Tree in 3-Connected 3-Regular Graphs

  • Haiyan KangAffiliated withSchool of Mathematics and System Sciences, Shandong University, Jinan, 250100
  • , Jichang WuAffiliated withSchool of Mathematics and System Sciences, Shandong University, Jinan, 250100
  • , Guojun LiAffiliated withSchool of Mathematics and System Sciences, Shandong University, Jinan, 250100CSBL, Department of Biochemistry and Molecular, Biology Institute of Bioinformatics, University of Georgia, GA 30602

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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(n 3) time algorithm to find all removable edges in G.

Keywords

3-connected 3-regular graph removable edge edge-vertex-cut fragment