Browsing Combinatorics and Optimization by Supervisor "Cheriyan, Joseph"
Now showing items 112 of 12

Approximating MinimumSize 2EdgeConnected and 2VertexConnected Spanning Subgraphs
(University of Waterloo, 20170427)We study the unweighted 2edgeconnected and 2vertexconnected spanning subgraph problems. A graph is 2edgeconnected if it is connected on removal of an edge, and it is 2vertexconnected if it is connected on removal ... 
Augmenting Trees to Achieve 2NodeConnectivity
(University of Waterloo, 20200902)This thesis focuses on the NodeConnectivity Tree Augmentation Problem (NCTAP), 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, 20160415)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, 20220817)A sieve method is in effect an application of the inclusionexclusion counting principle, and the estimation methods to avoid computing the explicit formula. Sieve methods have been used in number theory for over a hundred ... 
Combinatorially Thin Trees and Spectrally Thin Trees in Structured Graphs
(University of Waterloo, 20231219)Given a graph $G=(V,E)$, finding simpler estimates of $G$ with possibly fewer edges or vertices while capturing some of its specific properties has been used in order to design efficient algorithms. The concept of estimating ... 
Decompositionbased methods for Connectivity Augmentation Problems
(University of Waterloo, 20210903)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 kedgeconnected, and an additional ... 
Dynamic Pricing Schemes in Combinatorial Markets
(University of Waterloo, 20230501)In combinatorial markets where buyers are selfinterested, 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, 20180430)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, 153158). We ... 
The Matching Augmentation Problem: A 7/4Approximation Algorithm
(University of Waterloo, 20190523)We present a 7/4 approximation algorithm for the matching augmentation problem (MAP): given a multigraph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2edge connected ... 
Matchings and Representation Theory
(University of Waterloo, 20181220)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, 20180425)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, 20220817)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. ...