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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, Tutteâ€™s Wheelsand-Whirls Theorem proves that M has a 3-connected proper minor N with |E(M) âˆ’ E(N)| = 1 unless M is a wheel or a whirl. This paperâ€¦ (More)

- 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 ofâ€¦ (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 Mâˆ—(K3,k), M(Wk), M(Kk), the cycle matroid of the graph obtainedâ€¦ (More)

- Carolyn Chun, Deborah Chun, Dillon Mayhew, Stefan H. M. van Zwam
- Electr. J. Comb.
- 2015

If S is a set of matroids, then the matroid M is S-fragile if, for every element e âˆˆ E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend,â€¦ (More)

- 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,â€¦ (More)

- Carolyn Chun, James Oxley
- 2009

We prove that, for each positive integer k, every sufficiently large 3-connected regular matroid has a parallel minor isomorphic to Mâˆ—(K3,k), M(Wk), M(Kk), the cycle matroid of the graph obtainedâ€¦ (More)

- Carolyn Chun, Rhiannon Hall, Criel Merino, Iain Moffatt, Steven D. Noble
- Electr. J. Comb.
- 2018

The width of a delta-matroid is the difference in size between a maximal and minimal feasible set. We give a Rough Structure Theorem for delta-matroids that admit a twist of width one. We apply thisâ€¦ (More)

Acknowledgments This dissertation would not be possible without the boundless wisdom and patience (and of course mathematical insight) I leeched from my Ph.D. advisor, Dr. Bogdan Oporowski. Theâ€¦ (More)

- Carolyn Chun, Dillon Mayhew, James G. Oxley
- J. Comb. Theory, Ser. B
- 2016

In an earlier paper, we proved that an internally 4connected binary matroid with at least seven elements contains an internally 4-connected proper minor that is at most six elements smaller. Weâ€¦ (More)