Skip to main content
SpringerLink
Log in

Graphs G for which both G and G¯ are Contraction Critically k-Connected

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract.

 An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is called contraction critically k-connected. For k≥4, we prove that if both G and its complement G¯ are contraction critically k-connected, then |V(G)|<k 5/3+4k 3/2.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2–28–4 Tomigaya, Shibuya-ku, Tokyo 151–0063, Japan, , , , , , JP

    Jin Akiyama

  2. Department of Information and Communication Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182–8585, Japan, , , , , , JP

    Kiyoshi Ando

  3. Department of Mathematical Information Science, Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162–8601, Japan, , , , , , JP

    Yoshimi Egawa

Authors
  1. Jin Akiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kiyoshi Ando
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yoshimi Egawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: October, 2001 Final version received: September 18, 2002

AMS Classification: 05C40

Rights and permissions

Reprints and permissions

About this article

Cite this article

Akiyama, J., Ando, K. & Egawa, Y. Graphs G for which both G and G¯ are Contraction Critically k-Connected. Graphs Comb 18, 693–708 (2002). https://doi.org/10.1007/s003730200054

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s003730200054

Search

Navigation