Browsing Combinatorics and Optimization by Supervisor "Haxell, Penny"
Now showing items 1-5 of 5
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Correspondence Colouring and its Applications to List Colouring and Delay Colouring
(University of Waterloo, 2021-09-28)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, 2018-12-20)The Erdős pentagon problem asks about the maximum number of copies of C_5 that one can find in a triangle-free 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, 2019-08-23)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, 2016-05-17)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, 2020-01-10)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. ...