Now showing items 1-10 of 10

    • Approximating Minimum-Size 2-Edge-Connected and 2-Vertex-Connected Spanning Subgraphs 

      Narayan, Vishnu Verambudi (University of Waterloo, 2017-04-27)
      We study the unweighted 2-edge-connected and 2-vertex-connected spanning subgraph problems. A graph is 2-edge-connected if it is connected on removal of an edge, and it is 2-vertex-connected if it is connected on removal ...
    • Augmenting Trees to Achieve 2-Node-Connectivity 

      Grout, Logan (University of Waterloo, 2020-09-02)
      This thesis focuses on the Node-Connectivity Tree Augmentation Problem (NC-TAP), formally defined as follows. The first input of the problem is a graph G which has vertex set V and edge set E. We require |V| >= 3 to avoid ...
    • Brick Generation and Conformal Subgraphs 

      Kothari, Nishad (University of Waterloo, 2016-04-15)
      A nontrivial connected graph is matching covered if each of its edges lies in a perfect matching. Two types of decompositions of matching covered graphs, namely ear decompositions and tight cut decompositions, have played ...
    • Combinatorial Generalizations of Sieve Methods and Characterizing Hamiltonicity via Induced Subgraphs 

      Qu, Zishen (University of Waterloo, 2022-08-17)
      A sieve method is in effect an application of the inclusion-exclusion counting principle, and the estimation methods to avoid computing the explicit formula. Sieve methods have been used in number theory for over a hundred ...
    • Decomposition-based methods for Connectivity Augmentation Problems 

      Neogi, Rian (University of Waterloo, 2021-09-03)
      In this thesis, we study approximation algorithms for Connectivity Augmentation and related problems. In the Connectivity Augmentation problem, one is given a base graph G=(V,E) that is k-edge-connected, and an additional ...
    • Extensions of Galvin's Theorem 

      Levit, Maxwell (University of Waterloo, 2018-04-30)
      We discuss problems in list coloring with an emphasis on techniques that utilize oriented graphs. Our central theme is Galvin's resolution of the Dinitz problem (Galvin. J. Comb. Theory, Ser. B 63(1), 1995, 153--158). We ...
    • The Matching Augmentation Problem: A 7/4-Approximation Algorithm 

      Dippel, Jack (University of Waterloo, 2019-05-23)
      We present a 7/4 approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected ...
    • Matchings and Representation Theory 

      Lindzey, Nathan (University of Waterloo, 2018-12-20)
      In this thesis we investigate the algebraic properties of matchings via representation theory. We identify three scenarios in different areas of combinatorial mathematics where the algebraic structure of matchings gives ...
    • Thin Trees in Some Families of Graphs 

      Mousavi Haji, Seyyed Ramin (University of Waterloo, 2018-04-25)
      Let 𝐺=(𝑉,𝐸) be a graph and let 𝑇 be a spanning tree of 𝐺. The thinness parameter of 𝑇 denoted by 𝜌(𝑇) is the maximum over all cuts of the proportion of the edges of 𝑇 in the cut. Thin trees play an important role ...
    • The Traveling Tournament Problem 

      Bendayan, Salomon (University of Waterloo, 2022-08-17)
      In this thesis we study the Traveling Tournament problem (TTP) which asks to generate a feasible schedule for a sports league such that the total travel distance incurred by all teams throughout the season is minimized. ...

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