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- Carolyn Chun, Dillon Mayhew, James G. Oxley
- J. Comb. Theory, Ser. B
- 2011

Let M be a matroid. When M is 3-connected, Tutte’s WheelsandWhirls Theorem proves that M has a 3-connected proper minor N with exactly one element fewer than M unless M is a wheel or a whirl. I will present a corresponding result for internally 4-connected binary matroids. This presentation is based on joint work by myself, Dillon Mayhew, and James Oxley.

- Carolyn Chun, Guoli Ding, Bogdan Oporowski, Dirk L. Vertigan
- Journal of Graph Theory
- 2009

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 K4,k with a complete graph on the vertices of degree k, the k-partition triple fan with a… (More)

- Carolyn Chun
- 2013

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 coextension thereof, an internally 4-connected binary matroid M with an internally 4-connected proper minor N either has a proper internally 4-connected… (More)

- Carolyn Chun, Dillon Mayhew, James G. Oxley
- J. Comb. Theory, Ser. B
- 2012

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 4connected proper minor N either has a proper internally… (More)

- Carolyn Chun, Dillon Mayhew, James G. Oxley
- Eur. J. Comb.
- 2014

Let M and N be internally 4-connected binary matroids such that M has a proper N -minor, and |E(N)| ≥ 7. As part of our project to develop a splitter theorem for internally 4-connected binary matroids, we prove the following result: if M\e has no N -minor whenever e is in a triangle of M , and M/e has no N -minor whenever e is in a triad of M , then M has a… (More)

- Carolyn Chun, James G. Oxley
- Eur. J. Comb.
- 2011

We prove that, for each positive integer k, every sufficiently large 3-connected regular matroid has a parallel minor isomorphic to M∗(K3,k), M(Wk), M(Kk), the cycle matroid of the graph obtained from K2,k by adding paths through the vertices of each vertex class, or the cycle matroid of the graph obtained from K3,k by adding a complete graph on the vertex… (More)

We prove that, for each positive integer k, every sufficiently large 3-connected regular matroid has a parallel minor isomorphic to M∗(K3,k), M(Wk), M(Kk), the cycle matroid of the graph obtained from K2,k by adding paths through the vertices of each vertex class, or the cycle matroid of the graph obtained from K3,k by adding a complete graph on the vertex… (More)

- Carolyn Chun, Guoli Ding
- Discrete Mathematics
- 2010

A graph G is loosely-c-connected, or l-c-connected, if there exists a number d depending on G such that the deletion of fewer than c vertices from G leaves precisely one infinite component and a graph containing at most d vertices. In this paper, we give the structure of a set of l-c-connected infinite graphs that form an unavoidable set among the… (More)

- Carolyn Chun, Deborah Chun, Steven D. Noble, Steven D. Noblec
- 2017

We prove a splitter theorem for tight multimatroids, generalizing the corresponding result for matroids, obtained independently by Brylawski and Seymour. Further corollaries give splitter theorems for delta-matroids and ribbon graphs.

- Carolyn Chun, Rhiannon Hall, Criel Merino, Steven D. Noble
- Eur. J. Comb.
- 2017

We develop some basic tools to work with representable matroids of bounded tree-width and use them to prove that, for any prime power q and constant k, the characteristic polynomial of any loopless, GF (q)representable matroid with tree-width k has no real zero greater than qk−1.