Browsing Mathematics (Faculty of) by Supervisor "Haxell, Penny"
Now showing items 15 of 5

Correspondence Colouring and its Applications to List Colouring and Delay Colouring
(University of Waterloo, 20210928)In this thesis, we study correspondence colouring and its applications to list colouring and delay colouring. We give a detailed exposition of the paper of Dvořák, and Postle introducing correspondence colouring. Moreover, ... 
The Erdős Pentagon Problem
(University of Waterloo, 20181220)The Erdős pentagon problem asks about the maximum number of copies of C_5 that one can find in a trianglefree graph. This problem was posed in 1984, but was not resolved until 2012. In this thesis, we aim to capture the ... 
Finding Independent Transversals Efficiently
(University of Waterloo, 20190823)Let G be a graph and (V_1,...,V_m) be a vertex partition of G. An independent transversal (IT) of G with respect to (V_1,...,V_m) is an independent set {v_1,...,v_m} in G such that v_i is in V_i for each i in {1,...,m}. There ... 
Matchings and Covers in Hypergraphs
(University of Waterloo, 20160517)In this thesis, we study three variations of matching and covering problems in hypergraphs. The first is motivated by an old conjecture of Ryser which says that if $\mcH$ is an $r$uniform, $r$partite hypergraph which ... 
Santa Claus, Machine Scheduling and Bipartite Hypergraphs
(University of Waterloo, 20200110)Here we discuss two related discrete optimization problems, a prominent problem in scheduling theory, makespan minimization on unrelated parallel machines, and the other a fair allocation problem, the Santa Claus problem. ...