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Counterexamples to a conjecture of mader about cycles through specified vertices inn-edge-connected graphs

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Abstract

For each oddn≥3, we constructn-edge-connected graphsG with the following property: There are two verticesu andv inG such that for every cycleC inG passign throughu andv the graphG-E(C) is not (n-2)-edge-connected. HereE(C) denotes the set of edges ofC, and a cycle is allowed to pass through a vertex more than once.

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References

  1. Mader, W.: Paths in graphs, reducing the edge-connectivity only by two. Graphs Comb.1, 81–89 (1985)

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  2. Okamura, H.: Paths and edge-connectivity in graphs. J. of Comb. Theory (B),37, 151–172 (1984)

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  3. Okamura, H.: Paths ink-edge-connected graphs. J. of Comb. Theory (B),45, 345–355 (1988)

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Authors and Affiliations

  1. Institut für Mathematik, Universität Hannover, Welfengarten 1, W-3000, Hannover 1, Federal Republic of Germany

    Andreas Huck

  2. Faculty of Engineering, Osaka City University, 588, Osaka, Japan

    Haruko Okamura

Authors
  1. Andreas Huck
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  2. Haruko Okamura
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Huck, A., Okamura, H. Counterexamples to a conjecture of mader about cycles through specified vertices inn-edge-connected graphs. Graphs and Combinatorics 8, 253–258 (1992). https://doi.org/10.1007/BF02349962

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  • DOI: https://doi.org/10.1007/BF02349962

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