Now showing items 1-5 of 5

    • Correspondence Colouring and its Applications to List Colouring and Delay Colouring 

      Saleh, Rana (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 

      Siy, Kris (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 

      Graf, Alessandra (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 

      Szestopalow, Michael (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 

      Jay, Andrew (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. ...


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