Browsing Theses by Subject "matroids"
Now showing items 1-8 of 8
-
Disasters in Abstracting Combinatorial Properties of Linear Dependence
(University of Waterloo, 2020-05-15)A notion of geometric structure can be given to a set of points without using a coordinate system by instead describing geometric relations between finite combinations of elements. The fundamental problem is to then ... -
The Linkage Problem for Group-labelled Graphs
(University of Waterloo, 2009-09-24)This thesis aims to extend some of the results of the Graph Minors Project of Robertson and Seymour to "group-labelled graphs". Let $\Gamma$ be a group. A $\Gamma$-labelled graph is an oriented graph with its edges labelled ... -
Matrix Formulations of Matching Problems
(University of Waterloo, 2000)Finding the maximum size of a matching in an undirected graph and finding the maximum size of branching in a directed graph can be formulated as matrix rank problems. The Tutte matrix, introduced by Tutte as a representation ... -
Modularity and Structure in Matroids
(University of Waterloo, 2013-04-22)This thesis concerns sufficient conditions for a matroid to admit one of two types of structural characterization: a representation over a finite field or a description as a frame matroid. We call a restriction N of a ... -
On The Density of Binary Matroids Without a Given Minor
(University of Waterloo, 2016-12-21)This thesis is motivated by the following question: how many elements can a simple binary matroid with no $\PG(t,2)$-minor have? This is a natural analogue of questions asked about the density of graphs in minor-closed ... -
On the Excluded Minors for Dyadic Matroids
(University of Waterloo, 2019-01-17)The study of the class of dyadic matroids, the matroids representable over both $GF(3)$ and $GF(5)$, is a natural step to finding the excluded minors for $GF(5)$-representability. In this thesis we characterize the ternary ... -
Quadratically Dense Matroids
(University of Waterloo, 2020-07-08)This thesis is concerned with finding the maximum density of rank-$n$ matroids in a minor-closed class. The extremal function of a non-empty minor-closed class $\mathcal M$ of matroids which excludes a rank-2 uniform ... -
The search for an excluded minor characterization of ternary Rayleigh matroids
(University of Waterloo, 2008-01-24)Rayleigh matroids are a class of matroids with sets of bases that satisfy a strong negative correlation property. Interesting characteristics include the existence of an efficient algorithm for sampling the bases of a ...