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

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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.

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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
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  2. Kiyoshi Ando
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  3. Yoshimi Egawa
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Additional information

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

AMS Classification: 05C40

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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

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

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