# 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}
}
• Published 1 March 1993
• Mathematics
• J. Comb. Theory, Ser. B
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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## References

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• Mathematics
J. Comb. Theory, Ser. B
• 1994
A much better bound is proved on the tree-width of planar graphs with no minor isomorphic to a g × g grid and this is the best known bound.

### Graph Minors XV. Wagner's conjecture, manuscript

• Graph Minors XV. Wagner's conjecture, manuscript