Now showing items 1-8 of 8

    • Circle Graph Obstructions 

      Lee, Edward (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 

      Campbell, Rutger Theodoor Ronald Jansen van Doorn (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 

      Hoersch, Florian (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 

      Hill, Owen (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 

      Davies, James (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 

      McCarty, Rose (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 

      Wong, Chung-Yin (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 

      Shantanam, Abhinav (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 ...


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