Carolyn Chun

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A parallel minor is obtained from a graph by any sequence of edge contractions and parallel edge deletions. We prove that, for any positive integer k, every internally 4-connected graph of sufficiently high order contains a parallel minor isomorphic to a variation of K 4,k with a complete graph on the vertices of degree k, the k-partition triple fan with a(More)
Let M be a matroid. When M is 3-connected, Tutte's Wheels-and-Whirls Theorem proves that M has a 3-connected proper minor N with |E(M) − E(N)| = 1 unless M is a wheel or a whirl. This paper establishes a corresponding result for internally 4-connected binary matroids. In particular, we prove that if M is such a matroid, then M has an internally 4-connected(More)
This paper proves a preliminary step towards a splitter theorem for internally 4-connected binary matroids. In particular, we show that, provided M or M * is not a cubic Möbius or planar ladder or a certain coexten-sion thereof, an internally 4-connected binary matroid M with an internally 4-connected proper minor N either has a proper internally(More)
In our quest to find a splitter theorem for internally 4-connected binary matroids, we proved in the preceding paper in this series that, except when M or its dual is a cubic Möbius or planar ladder or a certain coextension thereof, an internally 4-connected binary matroid M with an internally 4-connected proper minor N either has a proper internally(More)
Let M be an internally 4-connected binary matroid and N be an internally 4-connected proper minor of M. In our search for a splitter theorem for internally 4-connected binary matroids, we proved in the third paper in this series that, except when M or its dual is a cubic Möbius or planar ladder or a certain coextension thereof, either M has a proper(More)