High Connectivity Keeping Sets In n-Connected Graphs

It is proved that for every positive integer k, every n-connected graph G of sufficiently large order contains a set W of k vertices such that GW is (n-2)-connected. It is shown that this does not remain true if we add the condition that G(W) is connected.

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Correspondence to W. Mader.

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Mader, W. High Connectivity Keeping Sets In n-Connected Graphs. Combinatorica 24, 441–458 (2004). https://doi.org/10.1007/s00493-004-0027-6

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Mathematics Subject Classification (2000):

  • 05C40
  • 05C35