Browsing Mathematics (Faculty of) by Subject "probabilistic method"

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Cliques, Degrees, and Coloring: Expanding the ω, Δ, χ paradigm

Kelly, Thomas (University of Waterloo, 2019-08-09)

Many of the most celebrated and influential results in graph coloring, such as Brooks' Theorem and Vizing's Theorem, relate a graph's chromatic number to its clique number or maximum degree. Currently, several of the most ...
On the Erdös-Turán conjecture and related results

Xiao, Stanley Yao (University of Waterloo, 2011-08-29)

The Erdös-Turán Conjecture, posed in 1941 in, states that if a subset B of natural numbers is such that every positive integer n can be written as the sum of a bounded number of terms from B, then the number of such ...
Uniform Generation of Graphical Realizations of Joint Degree Matrices

Zhou, Qianye (University of Waterloo, 2023-09-21)

In this thesis, we introduce JDM_GEN, an algorithm designed to uniformly generate graphical realizations of a given joint degree matrix. Amanatidis and Kleer previously employed an MCMC-based method to address this ...