# Typical Subgraphs of 3- and 4-Connected Graphs

@article{Oporowski1993TypicalSO, title={Typical Subgraphs of 3- and 4-Connected Graphs}, author={Bogdan Oporowski and James G. Oxley and Robin Thomas}, journal={J. Comb. Theory, Ser. B}, year={1993}, volume={57}, pages={239-257} }

Abstract We prove that, for every positive integer k , there is an integer N such that every 3-connected graph with at least N vertices has a minor isomorphic to the k -spoke wheel or K 3, k ; and that every internally 4-connected graph with at least N vertices has a minor isomorphic to the 2 k -spoke double wheel, the k -rung circular ladder, the k -rung Mobius ladder, or K 4, k . We also prove an analogous result for infinite graphs.

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