Browsing Mathematics (Faculty of) by Supervisor "Cheriyan, Joseph"
Now showing items 1-11 of 11
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Approximating Minimum-Size 2-Edge-Connected and 2-Vertex-Connected Spanning Subgraphs
(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
(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
(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
(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
(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 ... -
Dynamic Pricing Schemes in Combinatorial Markets
(University of Waterloo, 2023-05-01)In combinatorial markets where buyers are self-interested, the buyers may make purchases that lead to suboptimal item allocations. As a central coordinator, our goal is to impose prices on the items of the market so that ... -
Extensions of Galvin's Theorem
(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
(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
(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
(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
(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. ...