Show simple item record

dc.contributor.authorPivotto, Irene 21:03:11 (GMT) 21:03:11 (GMT)
dc.description.abstractIn this thesis we will present two main theorems that can be used to study 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'.en
dc.format.extent582923 bytes
dc.publisherUniversity of Waterlooen
dc.subjecteven cut matroiden
dc.titleOn Excluded Minors for Even Cut Matroidsen
dc.typeMaster Thesisen
dc.subject.programCombinatorics and Optimizationen and Optimizationen
uws-etd.degreeMaster of Mathematicsen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages