Now showing items 1-5 of 5

    • A Generalization to Signed Graphs of a Theorem of Sergey Norin and Robin Thomas 

      Horrocks, Courtney (University of Waterloo, 2019-12-19)
      In this thesis we characterize the minimal non-planar extensions of a signed graph. We consider the following question: Given a subdivision of a planar signed graph (G, Σ), what are the minimal structures that can be added ...
    • Ideal Clutters 

      Abdi, Ahmad (University of Waterloo, 2018-04-24)
      Let E be a finite set of elements, and let C be a family of subsets of E called members. We say that C is a clutter over ground set E if no member is contained in another. The clutter C is ideal if every extreme point of ...
    • Recognizing Even-Cycle and Even-Cut Matroids 

      Heo, Cheolwon (University of Waterloo, 2016-04-27)
      Even-cycle and even-cut matroids are classes of binary matroids that generalize respectively graphic and cographic matroids. We give algorithms to check membership for these classes of matroids. We assume that the matroids ...
    • Relaxations of the Maximum Flow Minimum Cut Property for Ideal Clutters 

      Ferchiou, Zouhaier (University of Waterloo, 2021-01-29)
      Given a family of sets, a covering problem consists of finding a minimum cost collection of elements that hits every set. This objective can always be bound by the maximum number of disjoint sets in the family, we refer ...
    • Representations of even-cycle and even-cut matroids 

      Heo, Cheolwon (University of Waterloo, 2021-08-27)
      In this thesis, two classes of binary matroids will be discussed: even-cycle and even-cut matroids, together with problems which are related to their graphical representations. Even-cycle and even-cut matroids can be ...

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