Finding Structures within Large Point Sets

We investigate two open problems in discrete geometry regarding how large subsets of sets of points need to be in order for certain structures to emerge. First of all there is the Erdős-Szekeres convex polygon problem, also known as the Happy Ending problem. Interestingly, there is a clear distinction between the number of points required to...

A Note on Integrity: ILP Modelling and Analysis on Graph Families

This thesis provides a fresh perspective on the (vertex) integrity of graphs, serving as a measure of network robustness. The study begins by introducing fundamental concepts and methods for evaluating the integrity of different graph families. An Integer Linear Programming (ILP) model, specifically designed for assessing integrity, is then...

Real Equiangular Lines

A set of lines passing through the origin in Euclidean space is called equiangular if the angle between any two lines is the same. The question of finding the maximum number of such lines, N(d) in any dimension d is an extensively studied problem. Closely related, is the problem of finding the maximum number of lines, N_α(d), such that the...

QAOA Mixing Hamiltonians for MinVertexCover

The minimum vertex cover problem (MinVertexCover) is an important optimization problem in graph theory, with applications in numerous fields outside of mathematics. As MinVertexCover is an NP-hard problem, there currently exists no efficient algorithm to find an optimal solution on arbitrary graphs. We consider quantum optimization algorithms,...

The "Number Hides Game" on a Tree: A bachelor thesis in game theory

The "Number Hides Game" (NHG) is 2-player game played on a board that consists of a row of p consecutive coins. Player I and player II simultaneously choose subsets of m and n consecutive coins respectively. Player II pays the number of coins that lie in the intersection of the subsets to player I. This thesis introduces basic knowledge from the...