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The Removable Edges and the Contractible Subgraphs of 5-Connected Graphs

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Abstract

An edge of a k-connected graph G is said to be k-removable if G − e is still k-connected. A subgraph H of a k-connected graph is said to be k-contractible if its contraction, that is, identification every component of H to a single vertex, results again a k-connected graph. In this paper, we show that there is either a removable edge or a contractible subgraph in a 5-connected graph which contains an edge with both endvertices have degree more than five. Thus every edge of minor minimal 5-connected graph is incident to at least one vertex of degree 5.

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Authors and Affiliations

  1. School of Mathematics Science, Guangxi Teachers Education University, Guangxi, 530001, Nanning, People’s Republic of China

    Chengfu Qin

  2. Department of Mathematics, Xiamen University, Xiamen, 310065, Fujian, People’s Republic of China

    Xiaofeng Guo

  3. Department of Information and Communication Engineering, The University of Electro-Communications, 1-5-1 Chofugaoku, Chofu, Tokyo, 182-8585, Japan

    Kiyoshi Ando

Authors
  1. Chengfu Qin
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  2. Xiaofeng Guo
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  3. Kiyoshi Ando
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Corresponding author

Correspondence to Chengfu Qin.

Additional information

The project supported by the National Natural Science Foundation of China (No. 11126321, No. 1161006); Natural Sciences Foundation of Guangxi Province (No. 2012GXNSFBA053005); The Scientific Research Foundation of Guangxi Education Committee (No.200103YB069).

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Qin, C., Guo, X. & Ando, K. The Removable Edges and the Contractible Subgraphs of 5-Connected Graphs. Graphs and Combinatorics 31, 243–254 (2015). https://doi.org/10.1007/s00373-013-1368-y

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  • DOI: https://doi.org/10.1007/s00373-013-1368-y

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