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2003, Doctor of Philosophy, Ohio State University, Mathematics.

The purpose of this dissertation is to generalize some important excluded-minor theorems for graphs to binary matroids.

Chapter 3 contains joint work with Hongxun Qin, in which we show that an internally 4-connected binary matroid with no *M(K _{5})*-,

In Chapter 4, it is shown that, except for 6 'small' known matroids, every internally 4-connected non-regular binary matroid has either a K͠_{5}- or a K͠_{5}^{*}-minor. Using this result, we obtain a computer-free proof of Dharmatilake's conjecture about the excluded minors for binary matroids with branch-width at most 3.

D.W. Hall proved that *K _{5}* is the only simple 3-connected graph with a

In chapter 6, it is shown that there are only finitely many non-regular internally 4-connected matroids in the class of binary matroids with no *M(K' _{3,3})*- or

In Chapter 7, we summarize the results and discuss about open problems. We are particularly interested in the class of binary matroids with no *M(K _{5})*- or

Neil Robertson (Advisor)

Thomas Dowling (Other)

Dijen Ray-Chaudhuri (Other)

Thomas Dowling (Other)

Dijen Ray-Chaudhuri (Other)

117 p.

Zhou, X. (2003). Some Excluded-Minor Theorems for Binary Matroids. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

Zhou, Xiangqian. "Some Excluded-Minor Theorems for Binary Matroids." Electronic Thesis or Dissertation. Ohio State University, 2003. OhioLINK Electronic Theses and Dissertations Center. 19 Feb 2018.

Zhou, Xiangqian "Some Excluded-Minor Theorems for Binary Matroids." Electronic Thesis or Dissertation. Ohio State University, 2003. https://etd.ohiolink.edu/