dc.contributor.author Pivotto, Irene dc.date.accessioned 2007-01-22 21:03:11 (GMT) dc.date.available 2007-01-22 21:03:11 (GMT) dc.date.issued 2007-01-22T21:03:11Z dc.date.submitted 2006 dc.identifier.uri http://hdl.handle.net/10012/2680 dc.description.abstract In this thesis we will present two main theorems that can be used to study en minor minimal non even cut matroids. Given any signed graph we can associate an even cut matroid. However, given an even cut matroid, there are in general, several signed graphs which represent that matroid. This is in contrast to, for instance graphic (or cographic) matroids, where all graphs corresponding to a particular graphic matroid are essentially equivalent. To tackle the multiple non equivalent representations of even cut matroids we use the concept of Stabilizer first introduced by Wittle. Namely, we show the following: given a "substantial" signed graph, which represents a matroid N that is a minor of a matroid M, then if the signed graph extends to a signed graph which represents M then it does so uniquely. Thus the representations of the small matroid determine the representations of the larger matroid containing it. This allows us to consider each representation of an even cut matroid essentially independently. Consider a small even cut matroid N that is a minor of a matroid M that is not an even cut matroid. We would like to prove that there exists a matroid N' which contains N and is contained in M such that the size of N' is small and such that N' is not an even cut matroid (this would imply in particular that there are only finitely many minimally non even cut matroids containing N). Clearly, none of the representations of N extends to M. We will show that (under certain technical conditions) starting from a fixed representation of N, there exists a matroid N' which contains N and is contained in M such that the size of N' is small and such that the representation of N does not extend to N'. dc.format.extent 582923 bytes dc.format.mimetype application/pdf dc.language.iso en en dc.publisher University of Waterloo en dc.subject even cut matroid en dc.title On Excluded Minors for Even Cut Matroids en dc.type Master Thesis en dc.pending false en dc.subject.program Combinatorics and Optimization en uws-etd.degree.department Combinatorics and Optimization en uws-etd.degree Master of Mathematics en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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