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Browsing Mathematics (Faculty of) by Supervisor "Geelen, Jim"
Now showing items 1-8 of 8
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Circle Graph Obstructions
(University of Waterloo, 2017-08-31)In this thesis we present a self-contained 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 excluded-minor characterization ... -
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 ... -
Extending Pappus' Theorem
(University of Waterloo, 2017-12-22)Let $M_1$ and $M_2$ be matroids such that $M_2$ arises from $M_1$ by relaxing a circuit-hyperplane. 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 ... -
Linearly-dense classes of matroids with bounded branch-width
(University of Waterloo, 2017-09-27)Let $M$ be a non-empty minor-closed class of matroids with bounded branch-width that does not contain arbitrarily large simple rank-$2$ matroids. For each non-negative integer $n$ we denote by $ex(n)$ the size of the ... -
Local properties of graphs with large chromatic number
(University of Waterloo, 2022-08-31)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 axis-aligned boxes and of lines in $\mathbb{R}^3$ ... -
Local Structure for Vertex-Minors
(University of Waterloo, 2021-10-12)This thesis is about a conjecture of Geelen on the structure of graphs with a forbidden vertex-minor; the conjecture is like the Graph Minors Structure Theorem of Robertson and Seymour but for vertex-minors instead of ... -
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 ... -
Unavoidable Minors of Large 5-Connected Graphs
(University of Waterloo, 2016-08-24)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 ...