, Volume 25, Issue 4, pp 557569
First online:
On the Structure of Contractible Edges in kconnected Partial ktrees
 N. S. NarayanaswamyAffiliated withDepartment of Computer Science and Engineering, Indian Institute of Technology Email author
 , N. SadagopanAffiliated withDepartment of Computer Science and Engineering, Indian Institute of Technology
 , L. Sunil ChandranAffiliated withComputer Science and Automation, Indian Institute of Science
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Contraction of an edge e merges its end points into a new single vertex, and each neighbor of one of the end points of e is a neighbor of the new vertex. An edge in a kconnected graph is contractible if its contraction does not result in a graph with lesser connectivity; otherwise the edge is called noncontractible. In this paper, we present results on the structure of contractible edges in ktrees and kconnected partial ktrees. Firstly, we show that an edge e in a ktree is contractible if and only if e belongs to exactly one (k + 1) clique. We use this characterization to show that the graph formed by contractible edges is a 2connected graph. We also show that there are at least V(G) + k − 2 contractible edges in a ktree. Secondly, we show that if an edge e in a partial ktree is contractible then e is contractible in any ktree which contains the partial ktree as an edge subgraph. We also construct a class of contraction critical 2kconnected partial 2ktrees.
Keywords
Connectivity Contraction Contractible edges Partial ktrees Title
 On the Structure of Contractible Edges in kconnected Partial ktrees
 Journal

Graphs and Combinatorics
Volume 25, Issue 4 , pp 557569
 Cover Date
 200911
 DOI
 10.1007/s003730090851y
 Print ISSN
 09110119
 Online ISSN
 14355914
 Publisher
 Springer Japan
 Additional Links
 Topics
 Keywords

 Connectivity
 Contraction
 Contractible edges
 Partial ktrees
 Industry Sectors
 Authors

 N. S. Narayanaswamy ^{(1)}
 N. Sadagopan ^{(1)}
 L. Sunil Chandran ^{(2)}
 Author Affiliations

 1. Department of Computer Science and Engineering, Indian Institute of Technology, Chennai, 600036, India
 2. Computer Science and Automation, Indian Institute of Science, Bangalore, 560012, India