Contractible edges in non-separating cycles


An edge of ak-connected graph is said to bek-contractible if the contraction of the edge results in ak-connected graph. We prove that every triangle-freek-connected graphG has an induced cycleC such that all edges ofC arek-contractible and such thatG−V(C) is (k−3)-connected (k≥4). This result unifies two theorems by Thomassen [5] and Egawa et. al. [3].

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Dedicated to Professor Toshiro Tsuzuku on his sixtieth birthday

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Egawa, Y., Saito, A. Contractible edges in non-separating cycles. Combinatorica 11, 389–392 (1991).

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AMS subject classification (1991)

  • 05 C 40
  • 05 C 38