Non-contractible edges in a 3-connected graph


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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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).

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Mathemacics Subject Classification (1991)

  • 05 C 40