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Non-contractible edges in a 3-connected graph

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Abstract

An edgee in a 3-connected graphG is contractible if the contraction ofe inG results in a 3-connected graph; otherwisee is non-contractible. In this paper, we prove that the number of non-contractible edges in a 3-connected graph of orderp≥5 is at most

$$3p - \left[ {\frac{3}{2}(\sqrt {24p + 25} - 5} \right],$$

and show that this upper bound is the best possible for infinitely many values ofp.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Science University of Tokyo, Shinjuku-ku, 162, Tokyo, JAPAN

    Yoshimi Egawa

  2. Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, 223, Yokohama-shi, Kanagawa, JAPAN

    Katsuhiro Ota

  3. Department of Mathematics, Nihon University, Sakurajosui 3-25-40 Setagaya-ku, 156, Tokyo, JAPAN

    Akira Saito

  4. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, USA

    Xingxing Yu

Authors
  1. Yoshimi Egawa
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  2. Katsuhiro Ota
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  3. Akira Saito
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  4. Xingxing Yu
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Additional information

Partially supported by Nihon University Research Grant B90-026

Partially supported by NSF under grant No. DMS-9105173

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Egawa, Y., Ota, K., Saito, A. et al. Non-contractible edges in a 3-connected graph. Combinatorica 15, 357–364 (1995). https://doi.org/10.1007/BF01299741

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  • DOI: https://doi.org/10.1007/BF01299741

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