Browsing Combinatorics and Optimization by Supervisor "Geelen, Jim"
Now showing items 18 of 8

Circle Graph Obstructions
(University of Waterloo, 20170831)In this thesis we present a selfcontained proof of Bouchet’s characterization of the class of circle graphs. The proof uses signed graphs and is analogous to Gerards’ graphic proof of Tutte’s excludedminor characterization ... 
Disasters in Abstracting Combinatorial Properties of Linear Dependence
(University of Waterloo, 20200515)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 ... 
Extending Pappus' Theorem
(University of Waterloo, 20171222)Let $M_1$ and $M_2$ be matroids such that $M_2$ arises from $M_1$ by relaxing a circuithyperplane. We will prove that if $M_1$ and $M_2$ are both representable over some finite field $GF(q)$, then $M_1$ and $M_2$ have ... 
Linearlydense classes of matroids with bounded branchwidth
(University of Waterloo, 20170927)Let $M$ be a nonempty minorclosed class of matroids with bounded branchwidth that does not contain arbitrarily large simple rank$2$ matroids. For each nonnegative integer $n$ we denote by $ex(n)$ the size of the ... 
Local properties of graphs with large chromatic number
(University of Waterloo, 20220831)This thesis deals with problems concerning the local properties of graphs with large chromatic number in hereditary classes of graphs. We construct intersection graphs of axisaligned boxes and of lines in $\mathbb{R}^3$ ... 
Local Structure for VertexMinors
(University of Waterloo, 20211012)This thesis is about a conjecture of Geelen on the structure of graphs with a forbidden vertexminor; the conjecture is like the Graph Minors Structure Theorem of Robertson and Seymour but for vertexminors instead of ... 
On the Excluded Minors for Dyadic Matroids
(University of Waterloo, 20190117)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 ... 
Unavoidable Minors of Large 5Connected Graphs
(University of Waterloo, 20160824)This thesis shows that, for every positive integer $n \geq 5$, there exists a positive integer $N$ such that every $5$connected graph with at least $N$ vertices has a minor isomorphic to one of thirty explicitly defined ...